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Popular >

integral of (e^y)^2

Solution

integral

(e^{y})^{2}

Solution

\frac{1}{2} e^{2 y} + C

Solution steps

\int (e^{y})^{2} d y

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{u ^{2}}{2}

Substitute back

u = e^{y}

= \frac{( e ^{y} ) ^{2}}{2}

Simplify

\frac{( e ^{y} ) ^{2}}{2} : \frac{1}{2} e^{2 y}

= \frac{1}{2} e^{2 y}

Add a constant to the solution

= \frac{1}{2} e^{2 y} + C

Graph

Popular Examples

integral of 1/((x+1))integral

\frac{1}{( x + 1 )}

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\frac{1}{( x ^{3} + x ^{2} + x )}

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\frac{cos ^{2} ( x )}{sin ^{2} ( x )}

integral of 1/((x^2-1))integral

\frac{1}{( x ^{2} - 1 )}

integral of 1/((x^2+3))integral

\frac{1}{( x ^{2} + 3 )}

Frequently Asked Questions (FAQ)

What is the integral of (e^y)^2 ?
The integral of (e^y)^2 is 1/2 e^{2y}+C