What is the integral of ((e)^x)^2 ?

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

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integral of ((e)^x)^2

integral

((e)^{x})^{2}

\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

cos^{2} (t) sin (t)

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

\frac{1}{36 + x ^{2}}

(x^{2}) sin (x)

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