Calculus Examples

Evaluate the Integral integral of e^(5x)(5) with respect to x
Step 1
Move to the left of .
Step 2
Since is constant with respect to , move out of the integral.
Step 3
Let . Then , so . Rewrite using and .
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Step 3.1
Let . Find .
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Step 3.1.1
Differentiate .
Step 3.1.2
Since is constant with respect to , the derivative of with respect to is .
Step 3.1.3
Differentiate using the Power Rule which states that is where .
Step 3.1.4
Multiply by .
Step 3.2
Rewrite the problem using and .
Step 4
Combine and .
Step 5
Since is constant with respect to , move out of the integral.
Step 6
Simplify.
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Step 6.1
Combine and .
Step 6.2
Cancel the common factor of .
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Step 6.2.1
Cancel the common factor.
Step 6.2.2
Rewrite the expression.
Step 6.3
Multiply by .
Step 7
The integral of with respect to is .
Step 8
Replace all occurrences of with .