Calculus Examples

Evaluate the Integral integral of (e^( square root of y))/( square root of y) with respect to y
Step 1
Apply basic rules of exponents.
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Step 1.1
Use to rewrite as .
Step 1.2
Use to rewrite as .
Step 1.3
Move out of the denominator by raising it to the power.
Step 1.4
Multiply the exponents in .
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Step 1.4.1
Apply the power rule and multiply exponents, .
Step 1.4.2
Combine and .
Step 1.4.3
Move the negative in front of the fraction.
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
Differentiate using the Power Rule which states that is where .
Step 2.1.3
To write as a fraction with a common denominator, multiply by .
Step 2.1.4
Combine and .
Step 2.1.5
Combine the numerators over the common denominator.
Step 2.1.6
Simplify the numerator.
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Step 2.1.6.1
Multiply by .
Step 2.1.6.2
Subtract from .
Step 2.1.7
Move the negative in front of the fraction.
Step 2.1.8
Simplify.
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Step 2.1.8.1
Rewrite the expression using the negative exponent rule .
Step 2.1.8.2
Multiply by .
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 .