Calculus Examples

Evaluate the Integral integral of 1/(e^(2x)) with respect to x
Step 1
Simplify the expression.
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Step 1.1
Negate the exponent of and move it out of the denominator.
Step 1.2
Simplify.
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Step 1.2.1
Multiply the exponents in .
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Step 1.2.1.1
Apply the power rule and multiply exponents, .
Step 1.2.1.2
Multiply by .
Step 1.2.2
Multiply by .
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
Since is constant with respect to , the derivative of with respect to is .
Step 2.1.3
Differentiate using the Power Rule which states that is where .
Step 2.1.4
Multiply by .
Step 2.2
Rewrite the problem using and .
Step 3
Simplify.
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Step 3.1
Move the negative in front of the fraction.
Step 3.2
Combine and .
Step 4
Since is constant with respect to , move out of the integral.
Step 5
Since is constant with respect to , move out of the integral.
Step 6
The integral of with respect to is .
Step 7
Simplify.
Step 8
Replace all occurrences of with .