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Calculus Examples
∫5x2(3x-4)(x-1)dx
Step 1
Since 5 is constant with respect to x, move 5 out of the integral.
5∫(x2(3x-4))(x-1)dx
Step 2
Step 2.1
Let u1=x-1. Find du1dx.
Step 2.1.1
Differentiate x-1.
ddx[x-1]
Step 2.1.2
By the Sum Rule, the derivative of x-1 with respect to x is ddx[x]+ddx[-1].
ddx[x]+ddx[-1]
Step 2.1.3
Differentiate using the Power Rule which states that ddx[xn] is nxn-1 where n=1.
1+ddx[-1]
Step 2.1.4
Since -1 is constant with respect to x, the derivative of -1 with respect to x is 0.
1+0
Step 2.1.5
Add 1 and 0.
1
1
Step 2.2
Rewrite the problem using u1 and du1.
5∫(u1+1)2(3(u1+1)-4)u1du1
5∫(u1+1)2(3(u1+1)-4)u1du1
Step 3
Step 3.1
Let u2=u1+1. Find du2du1.
Step 3.1.1
Differentiate u1+1.
ddu1[u1+1]
Step 3.1.2
By the Sum Rule, the derivative of u1+1 with respect to u1 is ddu1[u1]+ddu1[1].
ddu1[u1]+ddu1[1]
Step 3.1.3
Differentiate using the Power Rule which states that ddu1[u1n] is nu1n-1 where n=1.
1+ddu1[1]
Step 3.1.4
Since 1 is constant with respect to u1, the derivative of 1 with respect to u1 is 0.
1+0
Step 3.1.5
Add 1 and 0.
1
1
Step 3.2
Rewrite the problem using u2 and du2.
5∫u22(3u2-4)(u2-1)du2
5∫u22(3u2-4)(u2-1)du2
Step 4
Step 4.1
Let u3=u2-1. Find du3du2.
Step 4.1.1
Differentiate u2-1.
ddu2[u2-1]
Step 4.1.2
By the Sum Rule, the derivative of u2-1 with respect to u2 is ddu2[u2]+ddu2[-1].
ddu2[u2]+ddu2[-1]
Step 4.1.3
Differentiate using the Power Rule which states that ddu2[u2n] is nu2n-1 where n=1.
1+ddu2[-1]
Step 4.1.4
Since -1 is constant with respect to u2, the derivative of -1 with respect to u2 is 0.
1+0
Step 4.1.5
Add 1 and 0.
1
1
Step 4.2
Rewrite the problem using u3 and du3.
5∫(u3+1)2(3(u3+1)-4)u3du3
5∫(u3+1)2(3(u3+1)-4)u3du3
Step 5
Step 5.1
Rewrite (u3+1)2 as (u3+1)(u3+1).
5∫(u3+1)(u3+1)(3(u3+1)-4)u3du3
Step 5.2
Apply the distributive property.
5∫(u3(u3+1)+1(u3+1))(3(u3+1)-4)u3du3
Step 5.3
Apply the distributive property.
5∫(u3⋅u3+u3⋅1+1(u3+1))(3(u3+1)-4)u3du3
Step 5.4
Apply the distributive property.
5∫(u3⋅u3+u3⋅1+1u3+1⋅1)(3(u3+1)-4)u3du3
Step 5.5
Apply the distributive property.
5∫(u3⋅u3+u3⋅1+1u3+1⋅1)(3u3+3⋅1-4)u3du3
Step 5.6
Apply the distributive property.
5∫((u3⋅u3+u3⋅1)(3u3+3⋅1-4)+(1u3+1⋅1)(3u3+3⋅1-4))u3du3
Step 5.7
Apply the distributive property.
5∫(u3⋅u3(3u3+3⋅1-4)+u3⋅1(3u3+3⋅1-4)+(1u3+1⋅1)(3u3+3⋅1-4))u3du3
Step 5.8
Apply the distributive property.
5∫(u3⋅u3(3u3+3⋅1)+u3⋅u3⋅-4+u3⋅1(3u3+3⋅1-4)+(1u3+1⋅1)(3u3+3⋅1-4))u3du3
Step 5.9
Apply the distributive property.
5∫(u3⋅u3(3u3)+u3⋅u3(3⋅1)+u3⋅u3⋅-4+u3⋅1(3u3+3⋅1-4)+(1u3+1⋅1)(3u3+3⋅1-4))u3du3
Step 5.10
Apply the distributive property.
5∫(u3⋅u3(3u3)+u3⋅u3(3⋅1)+u3⋅u3⋅-4+u3⋅1(3u3+3⋅1)+u3⋅1⋅-4+(1u3+1⋅1)(3u3+3⋅1-4))u3du3
Step 5.11
Apply the distributive property.
5∫(u3⋅u3(3u3)+u3⋅u3(3⋅1)+u3⋅u3⋅-4+u3⋅1(3u3)+u3⋅1(3⋅1)+u3⋅1⋅-4+(1u3+1⋅1)(3u3+3⋅1-4))u3du3
Step 5.12
Apply the distributive property.
5∫(u3⋅u3(3u3)+u3⋅u3(3⋅1)+u3⋅u3⋅-4+u3⋅1(3u3)+u3⋅1(3⋅1)+u3⋅1⋅-4+1u3(3u3+3⋅1-4)+1⋅1(3u3+3⋅1-4))u3du3
Step 5.13
Apply the distributive property.
5∫(u3⋅u3(3u3)+u3⋅u3(3⋅1)+u3⋅u3⋅-4+u3⋅1(3u3)+u3⋅1(3⋅1)+u3⋅1⋅-4+1u3(3u3+3⋅1)+1u3⋅-4+1⋅1(3u3+3⋅1-4))u3du3
Step 5.14
Apply the distributive property.
5∫(u3⋅u3(3u3)+u3⋅u3(3⋅1)+u3⋅u3⋅-4+u3⋅1(3u3)+u3⋅1(3⋅1)+u3⋅1⋅-4+1u3(3u3)+1u3(3⋅1)+1u3⋅-4+1⋅1(3u3+3⋅1-4))u3du3
Step 5.15
Apply the distributive property.
5∫(u3⋅u3(3u3)+u3⋅u3(3⋅1)+u3⋅u3⋅-4+u3⋅1(3u3)+u3⋅1(3⋅1)+u3⋅1⋅-4+1u3(3u3)+1u3(3⋅1)+1u3⋅-4+1⋅1(3u3+3⋅1)+1⋅1⋅-4)u3du3
Step 5.16
Apply the distributive property.
5∫(u3⋅u3(3u3)+u3⋅u3(3⋅1)+u3⋅u3⋅-4+u3⋅1(3u3)+u3⋅1(3⋅1)+u3⋅1⋅-4+1u3(3u3)+1u3(3⋅1)+1u3⋅-4+1⋅1(3u3)+1⋅1(3⋅1)+1⋅1⋅-4)u3du3
Step 5.17
Apply the distributive property.
5∫(u3⋅u3(3u3)+u3⋅u3(3⋅1)+u3⋅u3⋅-4+u3⋅1(3u3)+u3⋅1(3⋅1)+u3⋅1⋅-4)u3+(1u3(3u3)+1u3(3⋅1)+1u3⋅-4+1⋅1(3u3)+1⋅1(3⋅1)+1⋅1⋅-4)u3du3
Step 5.18
Apply the distributive property.
5∫(u3⋅u3(3u3)+u3⋅u3(3⋅1)+u3⋅u3⋅-4)u3+(u3⋅1(3u3)+u3⋅1(3⋅1)+u3⋅1⋅-4)u3+(1u3(3u3)+1u3(3⋅1)+1u3⋅-4+1⋅1(3u3)+1⋅1(3⋅1)+1⋅1⋅-4)u3du3
Step 5.19
Apply the distributive property.
5∫(u3⋅u3(3u3)+u3⋅u3(3⋅1))u3+u3⋅u3⋅-4u3+(u3⋅1(3u3)+u3⋅1(3⋅1)+u3⋅1⋅-4)u3+(1u3(3u3)+1u3(3⋅1)+1u3⋅-4+1⋅1(3u3)+1⋅1(3⋅1)+1⋅1⋅-4)u3du3
Step 5.20
Apply the distributive property.
5∫u3⋅u3(3u3)u3+u3⋅u3(3⋅1)u3+u3⋅u3⋅-4u3+(u3⋅1(3u3)+u3⋅1(3⋅1)+u3⋅1⋅-4)u3+(1u3(3u3)+1u3(3⋅1)+1u3⋅-4+1⋅1(3u3)+1⋅1(3⋅1)+1⋅1⋅-4)u3du3
Step 5.21
Apply the distributive property.
5∫u3⋅u3(3u3)u3+u3⋅u3(3⋅1)u3+u3⋅u3⋅-4u3+(u3⋅1(3u3)+u3⋅1(3⋅1))u3+u3⋅1⋅-4u3+(1u3(3u3)+1u3(3⋅1)+1u3⋅-4+1⋅1(3u3)+1⋅1(3⋅1)+1⋅1⋅-4)u3du3
Step 5.22
Apply the distributive property.
5∫u3⋅u3(3u3)u3+u3⋅u3(3⋅1)u3+u3⋅u3⋅-4u3+u3⋅1(3u3)u3+u3⋅1(3⋅1)u3+u3⋅1⋅-4u3+(1u3(3u3)+1u3(3⋅1)+1u3⋅-4+1⋅1(3u3)+1⋅1(3⋅1)+1⋅1⋅-4)u3du3
Step 5.23
Apply the distributive property.
5∫u3⋅u3(3u3)u3+u3⋅u3(3⋅1)u3+u3⋅u3⋅-4u3+u3⋅1(3u3)u3+u3⋅1(3⋅1)u3+u3⋅1⋅-4u3+(1u3(3u3)+1u3(3⋅1)+1u3⋅-4)u3+(1⋅1(3u3)+1⋅1(3⋅1)+1⋅1⋅-4)u3du3
Step 5.24
Apply the distributive property.
5∫u3⋅u3(3u3)u3+u3⋅u3(3⋅1)u3+u3⋅u3⋅-4u3+u3⋅1(3u3)u3+u3⋅1(3⋅1)u3+u3⋅1⋅-4u3+(1u3(3u3)+1u3(3⋅1))u3+1u3⋅-4u3+(1⋅1(3u3)+1⋅1(3⋅1)+1⋅1⋅-4)u3du3
Step 5.25
Apply the distributive property.
5∫u3⋅u3(3u3)u3+u3⋅u3(3⋅1)u3+u3⋅u3⋅-4u3+u3⋅1(3u3)u3+u3⋅1(3⋅1)u3+u3⋅1⋅-4u3+1u3(3u3)u3+1u3(3⋅1)u3+1u3⋅-4u3+(1⋅1(3u3)+1⋅1(3⋅1)+1⋅1⋅-4)u3du3
Step 5.26
Apply the distributive property.
5∫u3⋅u3(3u3)u3+u3⋅u3(3⋅1)u3+u3⋅u3⋅-4u3+u3⋅1(3u3)u3+u3⋅1(3⋅1)u3+u3⋅1⋅-4u3+1u3(3u3)u3+1u3(3⋅1)u3+1u3⋅-4u3+(1⋅1(3u3)+1⋅1(3⋅1))u3+1⋅1⋅-4u3du3
Step 5.27
Apply the distributive property.
5∫u3⋅u3(3u3)u3+u3⋅u3(3⋅1)u3+u3⋅u3⋅-4u3+u3⋅1(3u3)u3+u3⋅1(3⋅1)u3+u3⋅1⋅-4u3+1u3(3u3)u3+1u3(3⋅1)u3+1u3⋅-4u3+1⋅1(3u3)u3+1⋅1(3⋅1)u3+1⋅1⋅-4u3du3
Step 5.28
Move u3.
5∫u3⋅3u3⋅u3⋅u3+u3⋅u3(3⋅1)u3+u3⋅u3⋅-4u3+u3⋅1(3u3)u3+u3⋅1(3⋅1)u3+u3⋅1⋅-4u3+1u3(3u3)u3+1u3(3⋅1)u3+1u3⋅-4u3+1⋅1(3u3)u3+1⋅1(3⋅1)u3+1⋅1⋅-4u3du3
Step 5.29
Reorder u3 and 3.
5∫3⋅u3⋅u3⋅u3⋅u3+u3⋅u3(3⋅1)u3+u3⋅u3⋅-4u3+u3⋅1(3u3)u3+u3⋅1(3⋅1)u3+u3⋅1⋅-4u3+1u3(3u3)u3+1u3(3⋅1)u3+1u3⋅-4u3+1⋅1(3u3)u3+1⋅1(3⋅1)u3+1⋅1⋅-4u3du3
Step 5.30
Move u3.
5∫3⋅u3⋅u3⋅u3⋅u3+u3⋅3⋅1u3⋅u3+u3⋅u3⋅-4u3+u3⋅1(3u3)u3+u3⋅1(3⋅1)u3+u3⋅1⋅-4u3+1u3(3u3)u3+1u3(3⋅1)u3+1u3⋅-4u3+1⋅1(3u3)u3+1⋅1(3⋅1)u3+1⋅1⋅-4u3du3
Step 5.31
Move u3.
5∫3⋅u3⋅u3⋅u3⋅u3+3⋅1u3⋅u3⋅u3+u3⋅u3⋅-4u3+u3⋅1(3u3)u3+u3⋅1(3⋅1)u3+u3⋅1⋅-4u3+1u3(3u3)u3+1u3(3⋅1)u3+1u3⋅-4u3+1⋅1(3u3)u3+1⋅1(3⋅1)u3+1⋅1⋅-4u3du3
Step 5.32
Move u3.
5∫3⋅u3⋅u3⋅u3⋅u3+3⋅1u3⋅u3⋅u3+u3⋅-4u3⋅u3+u3⋅1(3u3)u3+u3⋅1(3⋅1)u3+u3⋅1⋅-4u3+1u3(3u3)u3+1u3(3⋅1)u3+1u3⋅-4u3+1⋅1(3u3)u3+1⋅1(3⋅1)u3+1⋅1⋅-4u3du3
Step 5.33
Reorder u3 and -4.
5∫3⋅u3⋅u3⋅u3⋅u3+3⋅1u3⋅u3⋅u3-4⋅u3⋅u3⋅u3+u3⋅1(3u3)u3+u3⋅1(3⋅1)u3+u3⋅1⋅-4u3+1u3(3u3)u3+1u3(3⋅1)u3+1u3⋅-4u3+1⋅1(3u3)u3+1⋅1(3⋅1)u3+1⋅1⋅-4u3du3
Step 5.34
Reorder u3 and 1.
5∫3⋅u3⋅u3⋅u3⋅u3+3⋅1u3⋅u3⋅u3-4⋅u3⋅u3⋅u3+1⋅u3(3u3)u3+u3⋅1(3⋅1)u3+u3⋅1⋅-4u3+1u3(3u3)u3+1u3(3⋅1)u3+1u3⋅-4u3+1⋅1(3u3)u3+1⋅1(3⋅1)u3+1⋅1⋅-4u3du3
Step 5.35
Move u3.
5∫3⋅u3⋅u3⋅u3⋅u3+3⋅1u3⋅u3⋅u3-4⋅u3⋅u3⋅u3+1⋅3u3⋅u3⋅u3+u3⋅1(3⋅1)u3+u3⋅1⋅-4u3+1u3(3u3)u3+1u3(3⋅1)u3+1u3⋅-4u3+1⋅1(3u3)u3+1⋅1(3⋅1)u3+1⋅1⋅-4u3du3
Step 5.36
Reorder u3 and 1.
5∫3⋅u3⋅u3⋅u3⋅u3+3⋅1u3⋅u3⋅u3-4⋅u3⋅u3⋅u3+1⋅3u3⋅u3⋅u3+1⋅u3(3⋅1)u3+u3⋅1⋅-4u3+1u3(3u3)u3+1u3(3⋅1)u3+1u3⋅-4u3+1⋅1(3u3)u3+1⋅1(3⋅1)u3+1⋅1⋅-4u3du3
Step 5.37
Move u3.
5∫3⋅u3⋅u3⋅u3⋅u3+3⋅1u3⋅u3⋅u3-4⋅u3⋅u3⋅u3+1⋅3u3⋅u3⋅u3+1⋅3⋅1u3⋅u3+u3⋅1⋅-4u3+1u3(3u3)u3+1u3(3⋅1)u3+1u3⋅-4u3+1⋅1(3u3)u3+1⋅1(3⋅1)u3+1⋅1⋅-4u3du3
Step 5.38
Reorder u3 and 1.
5∫3⋅u3⋅u3⋅u3⋅u3+3⋅1u3⋅u3⋅u3-4⋅u3⋅u3⋅u3+1⋅3u3⋅u3⋅u3+1⋅3⋅1u3⋅u3+1⋅u3⋅-4u3+1u3(3u3)u3+1u3(3⋅1)u3+1u3⋅-4u3+1⋅1(3u3)u3+1⋅1(3⋅1)u3+1⋅1⋅-4u3du3
Step 5.39
Move u3.
5∫3⋅u3⋅u3⋅u3⋅u3+3⋅1u3⋅u3⋅u3-4⋅u3⋅u3⋅u3+1⋅3u3⋅u3⋅u3+1⋅3⋅1u3⋅u3+1⋅-4u3⋅u3+1u3(3u3)u3+1u3(3⋅1)u3+1u3⋅-4u3+1⋅1(3u3)u3+1⋅1(3⋅1)u3+1⋅1⋅-4u3du3
Step 5.40
Move u3.
5∫3⋅u3⋅u3⋅u3⋅u3+3⋅1u3⋅u3⋅u3-4⋅u3⋅u3⋅u3+1⋅3u3⋅u3⋅u3+1⋅3⋅1u3⋅u3+1⋅-4u3⋅u3+1⋅3u3⋅u3⋅u3+1u3(3⋅1)u3+1u3⋅-4u3+1⋅1(3u3)u3+1⋅1(3⋅1)u3+1⋅1⋅-4u3du3
Step 5.41
Move u3.
5∫3⋅u3⋅u3⋅u3⋅u3+3⋅1u3⋅u3⋅u3-4⋅u3⋅u3⋅u3+1⋅3u3⋅u3⋅u3+1⋅3⋅1u3⋅u3+1⋅-4u3⋅u3+1⋅3u3⋅u3⋅u3+1⋅3⋅1u3⋅u3+1u3⋅-4u3+1⋅1(3u3)u3+1⋅1(3⋅1)u3+1⋅1⋅-4u3du3
Step 5.42
Move u3.
5∫3⋅u3⋅u3⋅u3⋅u3+3⋅1u3⋅u3⋅u3-4⋅u3⋅u3⋅u3+1⋅3u3⋅u3⋅u3+1⋅3⋅1u3⋅u3+1⋅-4u3⋅u3+1⋅3u3⋅u3⋅u3+1⋅3⋅1u3⋅u3+1⋅-4u3⋅u3+1⋅1(3u3)u3+1⋅1(3⋅1)u3+1⋅1⋅-4u3du3
Step 5.43
Raise u3 to the power of 1.
5∫3(u31u3)u3⋅u3+3⋅1u3⋅u3⋅u3-4u3⋅u3⋅u3+1⋅3u3⋅u3⋅u3+1⋅3⋅1u3⋅u3+1⋅-4u3⋅u3+1⋅3u3⋅u3⋅u3+1⋅3⋅1u3⋅u3+1⋅-4u3⋅u3+1⋅1⋅3u3⋅u3+1⋅1⋅3⋅1u3+1⋅1⋅-4u3du3
Step 5.44
Raise u3 to the power of 1.
5∫3(u31u31)u3⋅u3+3⋅1u3⋅u3⋅u3-4u3⋅u3⋅u3+1⋅3u3⋅u3⋅u3+1⋅3⋅1u3⋅u3+1⋅-4u3⋅u3+1⋅3u3⋅u3⋅u3+1⋅3⋅1u3⋅u3+1⋅-4u3⋅u3+1⋅1⋅3u3⋅u3+1⋅1⋅3⋅1u3+1⋅1⋅-4u3du3
Step 5.45
Use the power rule aman=am+n to combine exponents.
5∫3u31+1u3⋅u3+3⋅1u3⋅u3⋅u3-4u3⋅u3⋅u3+1⋅3u3⋅u3⋅u3+1⋅3⋅1u3⋅u3+1⋅-4u3⋅u3+1⋅3u3⋅u3⋅u3+1⋅3⋅1u3⋅u3+1⋅-4u3⋅u3+1⋅1⋅3u3⋅u3+1⋅1⋅3⋅1u3+1⋅1⋅-4u3du3
Step 5.46
Add 1 and 1.
5∫3u32u3⋅u3+3⋅1u3⋅u3⋅u3-4u3⋅u3⋅u3+1⋅3u3⋅u3⋅u3+1⋅3⋅1u3⋅u3+1⋅-4u3⋅u3+1⋅3u3⋅u3⋅u3+1⋅3⋅1u3⋅u3+1⋅-4u3⋅u3+1⋅1⋅3u3⋅u3+1⋅1⋅3⋅1u3+1⋅1⋅-4u3du3
Step 5.47
Raise u3 to the power of 1.
5∫3(u32u31)u3+3⋅1u3⋅u3⋅u3-4u3⋅u3⋅u3+1⋅3u3⋅u3⋅u3+1⋅3⋅1u3⋅u3+1⋅-4u3⋅u3+1⋅3u3⋅u3⋅u3+1⋅3⋅1u3⋅u3+1⋅-4u3⋅u3+1⋅1⋅3u3⋅u3+1⋅1⋅3⋅1u3+1⋅1⋅-4u3du3
Step 5.48
Use the power rule to combine exponents.
Step 5.49
Add and .
Step 5.50
Raise to the power of .
Step 5.51
Use the power rule to combine exponents.
Step 5.52
Add and .
Step 5.53
Multiply by .
Step 5.54
Raise to the power of .
Step 5.55
Raise to the power of .
Step 5.56
Use the power rule to combine exponents.
Step 5.57
Add and .
Step 5.58
Raise to the power of .
Step 5.59
Use the power rule to combine exponents.
Step 5.60
Add and .
Step 5.61
Raise to the power of .
Step 5.62
Raise to the power of .
Step 5.63
Use the power rule to combine exponents.
Step 5.64
Add and .
Step 5.65
Raise to the power of .
Step 5.66
Use the power rule to combine exponents.
Step 5.67
Add and .
Step 5.68
Subtract from .
Step 5.69
Multiply by .
Step 5.70
Raise to the power of .
Step 5.71
Raise to the power of .
Step 5.72
Use the power rule to combine exponents.
Step 5.73
Add and .
Step 5.74
Raise to the power of .
Step 5.75
Use the power rule to combine exponents.
Step 5.76
Add and .
Step 5.77
Multiply by .
Step 5.78
Multiply by .
Step 5.79
Raise to the power of .
Step 5.80
Raise to the power of .
Step 5.81
Use the power rule to combine exponents.
Step 5.82
Add and .
Step 5.83
Multiply by .
Step 5.84
Raise to the power of .
Step 5.85
Raise to the power of .
Step 5.86
Use the power rule to combine exponents.
Step 5.87
Add and .
Step 5.88
Subtract from .
Step 5.89
Add and .
Step 5.90
Multiply by .
Step 5.91
Raise to the power of .
Step 5.92
Raise to the power of .
Step 5.93
Use the power rule to combine exponents.
Step 5.94
Add and .
Step 5.95
Raise to the power of .
Step 5.96
Use the power rule to combine exponents.
Step 5.97
Add and .
Step 5.98
Multiply by .
Step 5.99
Multiply by .
Step 5.100
Raise to the power of .
Step 5.101
Raise to the power of .
Step 5.102
Use the power rule to combine exponents.
Step 5.103
Add and .
Step 5.104
Multiply by .
Step 5.105
Raise to the power of .
Step 5.106
Raise to the power of .
Step 5.107
Use the power rule to combine exponents.
Step 5.108
Add and .
Step 5.109
Subtract from .
Step 5.110
Multiply by .
Step 5.111
Multiply by .
Step 5.112
Raise to the power of .
Step 5.113
Raise to the power of .
Step 5.114
Use the power rule to combine exponents.
Step 5.115
Add and .
Step 5.116
Multiply by .
Step 5.117
Multiply by .
Step 5.118
Multiply by .
Step 5.119
Multiply by .
Step 5.120
Multiply by .
Step 5.121
Subtract from .
Step 5.122
Add and .
Step 5.123
Move .
Step 5.124
Move .
Step 5.125
Add and .
Step 5.126
Subtract from .
Step 6
Split the single integral into multiple integrals.
Step 7
Since is constant with respect to , move out of the integral.
Step 8
By the Power Rule, the integral of with respect to is .
Step 9
Since is constant with respect to , move out of the integral.
Step 10
By the Power Rule, the integral of with respect to is .
Step 11
By the Power Rule, the integral of with respect to is .
Step 12
Step 12.1
Combine and .
Step 12.2
Combine and .
Step 12.3
Combine and .
Step 13
Since is constant with respect to , move out of the integral.
Step 14
By the Power Rule, the integral of with respect to is .
Step 15
Step 15.1
Combine and .
Step 15.2
Simplify.
Step 16
Step 16.1
Replace all occurrences of with .
Step 16.2
Replace all occurrences of with .
Step 16.3
Replace all occurrences of with .
Step 17
Reorder terms.