Calculus Examples

Evaluate the Integral integral of (x^3+3)^3x^5 with respect to x
Step 1
Expand .
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Step 1.1
Use the Binomial Theorem.
Step 1.2
Rewrite the exponentiation as a product.
Step 1.3
Rewrite the exponentiation as a product.
Step 1.4
Rewrite the exponentiation as a product.
Step 1.5
Rewrite the exponentiation as a product.
Step 1.6
Rewrite the exponentiation as a product.
Step 1.7
Rewrite the exponentiation as a product.
Step 1.8
Apply the distributive property.
Step 1.9
Apply the distributive property.
Step 1.10
Apply the distributive property.
Step 1.11
Move .
Step 1.12
Move .
Step 1.13
Move .
Step 1.14
Use the power rule to combine exponents.
Step 1.15
Add and .
Step 1.16
Use the power rule to combine exponents.
Step 1.17
Add and .
Step 1.18
Use the power rule to combine exponents.
Step 1.19
Add and .
Step 1.20
Multiply by .
Step 1.21
Use the power rule to combine exponents.
Step 1.22
Add and .
Step 1.23
Use the power rule to combine exponents.
Step 1.24
Add and .
Step 1.25
Multiply by .
Step 1.26
Multiply by .
Step 1.27
Use the power rule to combine exponents.
Step 1.28
Add and .
Step 1.29
Multiply by .
Step 1.30
Multiply by .
Step 2
Split the single integral into multiple integrals.
Step 3
By the Power Rule, the integral of with respect to is .
Step 4
Since is constant with respect to , move out of the integral.
Step 5
By the Power Rule, the integral of with respect to is .
Step 6
Since is constant with respect to , move out of the integral.
Step 7
By the Power Rule, the integral of with respect to is .
Step 8
Since is constant with respect to , move out of the integral.
Step 9
By the Power Rule, the integral of with respect to is .
Step 10
Simplify.
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Step 10.1
Simplify.
Step 10.2
Simplify.
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Step 10.2.1
Combine and .
Step 10.2.2
Combine and .
Step 10.2.3
Cancel the common factor of and .
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Step 10.2.3.1
Factor out of .
Step 10.2.3.2
Cancel the common factors.
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Step 10.2.3.2.1
Factor out of .
Step 10.2.3.2.2
Cancel the common factor.
Step 10.2.3.2.3
Rewrite the expression.
Step 10.3
Reorder terms.