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Popular >

integral of (e^y)^2

Solution

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

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

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Frequently Asked Questions (FAQ)

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