Calculus Examples

Evaluate the Integral integral of x(90x^2+30x) with respect to x
Step 1
Simplify.
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Step 1.1
Apply the distributive property.
Step 1.2
Reorder and .
Step 1.3
Reorder and .
Step 1.4
Raise to the power of .
Step 1.5
Use the power rule to combine exponents.
Step 1.6
Add and .
Step 1.7
Raise to the power of .
Step 1.8
Raise to the power of .
Step 1.9
Use the power rule to combine exponents.
Step 1.10
Add and .
Step 2
Split the single integral into multiple integrals.
Step 3
Since is constant with respect to , move out of the integral.
Step 4
By the Power Rule, the integral of with respect to is .
Step 5
Since is constant with respect to , move out of the integral.
Step 6
By the Power Rule, the integral of with respect to is .
Step 7
Simplify.
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Step 7.1
Simplify.
Step 7.2
Simplify.
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Step 7.2.1
Combine and .
Step 7.2.2
Cancel the common factor of and .
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Step 7.2.2.1
Factor out of .
Step 7.2.2.2
Cancel the common factors.
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Step 7.2.2.2.1
Factor out of .
Step 7.2.2.2.2
Cancel the common factor.
Step 7.2.2.2.3
Rewrite the expression.
Step 7.2.3
Combine and .
Step 7.2.4
Cancel the common factor of and .
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Step 7.2.4.1
Factor out of .
Step 7.2.4.2
Cancel the common factors.
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Step 7.2.4.2.1
Factor out of .
Step 7.2.4.2.2
Cancel the common factor.
Step 7.2.4.2.3
Rewrite the expression.
Step 7.2.4.2.4
Divide by .