Calculus Examples

Evaluate the Integral integral of arccot(x) with respect to x
Step 1
Integrate by parts using the formula , where and .
Step 2
Combine and .
Step 3
Since is constant with respect to , move out of the integral.
Step 4
Simplify.
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Step 4.1
Multiply by .
Step 4.2
Multiply by .
Step 5
Let . Then , so . Rewrite using and .
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Step 5.1
Let . Find .
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Step 5.1.1
Differentiate .
Step 5.1.2
By the Sum Rule, the derivative of with respect to is .
Step 5.1.3
Since is constant with respect to , the derivative of with respect to is .
Step 5.1.4
Differentiate using the Power Rule which states that is where .
Step 5.1.5
Add and .
Step 5.2
Rewrite the problem using and .
Step 6
Simplify.
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Step 6.1
Multiply by .
Step 6.2
Move to the left of .
Step 7
Since is constant with respect to , move out of the integral.
Step 8
The integral of with respect to is .
Step 9
Simplify.
Step 10
Replace all occurrences of with .