Calculus Examples

Evaluate the Integral integral from e to e^2 of 1/(x natural log of x) with respect to x
Step 1
Let . Then , so . Rewrite using and .
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Step 1.1
Let . Find .
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Step 1.1.1
Differentiate .
Step 1.1.2
The derivative of with respect to is .
Step 1.2
Substitute the lower limit in for in .
Step 1.3
The natural logarithm of is .
Step 1.4
Substitute the upper limit in for in .
Step 1.5
Simplify.
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Step 1.5.1
Use logarithm rules to move out of the exponent.
Step 1.5.2
The natural logarithm of is .
Step 1.5.3
Multiply by .
Step 1.6
The values found for and will be used to evaluate the definite integral.
Step 1.7
Rewrite the problem using , , and the new limits of integration.
Step 2
The integral of with respect to is .
Step 3
Evaluate at and at .
Step 4
Use the quotient property of logarithms, .
Step 5
Simplify.
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Step 5.1
The absolute value is the distance between a number and zero. The distance between and is .
Step 5.2
The absolute value is the distance between a number and zero. The distance between and is .
Step 5.3
Divide by .
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form: