Calculus Examples

Evaluate the Integral integral of 1/(x^2)*cos(1/x) with respect to x
Step 1
Combine and .
Step 2
Let . Then , so . Rewrite using and .
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Step 2.1
Let . Find .
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Step 2.1.1
Differentiate .
Step 2.1.2
Rewrite as .
Step 2.1.3
Differentiate using the Power Rule which states that is where .
Step 2.1.4
Rewrite the expression using the negative exponent rule .
Step 2.2
Rewrite the problem using and .
Step 3
Since is constant with respect to , move out of the integral.
Step 4
The integral of with respect to is .
Step 5
Simplify.
Step 6
Replace all occurrences of with .