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Popular >

integral of (e^x)^2

Solution

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

Solution

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

Solution steps

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

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^{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

Popular Examples

sum from n=1 to infinity of 23(2/5)^n

n = 1 \sum \infty 23 (\frac{2}{5})^{n}

integral of (e^x)/(3-e^{2x)}

\int \frac{e ^{x}}{3 - e ^{2 x}} d x

y (x + 3) + y^{^{'}} = 0

tangent of 8+2x+xe^x tangent of

8 + 2 x + x e^{x}

tangent of f(x)=(4x)/(x+3),\at x=-5 tangent of

f (x) = \frac{4 x}{x + 3}, at x = - 5

Frequently Asked Questions (FAQ)

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