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Popular Calculus >

integral of (e^x)^2

Solution

integral

(e^{x})^{2}

Solution

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

Solution steps

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

Apply u-substitution

= \int u d u

Apply the Power Rule

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

Substitute back

u = e^{x}

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

Simplify

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

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

Add a constant to the solution

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

Graph

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integral of 1+x

in t e g r a l 1 + x

integral of 1-cos^2(x)

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

Frequently Asked Questions (FAQ)

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