Calculus Examples

Evaluate the Integral integral of (4x+2)/(x^2+x+5) with respect to x
Step 1
Factor out of .
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Step 1.1
Factor out of .
Step 1.2
Factor out of .
Step 1.3
Factor out 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
By the Sum Rule, 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
Differentiate using the Power Rule which states that is where .
Step 3.1.5
Since is constant with respect to , the derivative of with respect to is .
Step 3.1.6
Add and .
Step 3.2
Rewrite the problem using and .
Step 4
The integral of with respect to is .
Step 5
Simplify.
Step 6
Replace all occurrences of with .