Calculus Examples

Evaluate the Integral integral of (x^2+5)^3 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
Move .
Step 1.9
Move .
Step 1.10
Move .
Step 1.11
Use the power rule to combine exponents.
Step 1.12
Add and .
Step 1.13
Use the power rule to combine exponents.
Step 1.14
Add and .
Step 1.15
Multiply by .
Step 1.16
Use the power rule to combine exponents.
Step 1.17
Add and .
Step 1.18
Multiply by .
Step 1.19
Multiply by .
Step 1.20
Multiply by .
Step 1.21
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
Apply the constant rule.
Step 9
Simplify.
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Step 9.1
Simplify.
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Step 9.1.1
Combine and .
Step 9.1.2
Combine and .
Step 9.2
Simplify.
Step 9.3
Reorder terms.