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Popular Calculus >

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

Apply the Power Rule

= \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^3+x^2+x))

in t e g r a l \frac{1}{( x ^{3} + x ^{2} + x )}

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

in t e g r a l \frac{1}{( x ^{2} - 1 )}

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

in t e g r a l \frac{x ^{- 1}}{x ^{2}}

integral of-sin^2(x)+tan^2(x)

in t e g r a l - sin^{2} (x) + tan^{2} (x)

integral of 1/((x+2))

in t e g r a l \frac{1}{( x + 2 )}

Frequently Asked Questions (FAQ)

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