en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of (e^t)^2

Solution

integral

(e^{t})^{2}

Solution

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

Solution steps

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

Apply u-substitution

= \int u d u

Apply the Power Rule

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

Substitute back

u = e^{t}

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

Simplify

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

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

Add a constant to the solution

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

Graph

Popular Examples

integral of e^{1/x}x

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

integral of t/6

integral of 1/((1+x^3))

integral of (3x-5)^{-2}

Frequently Asked Questions (FAQ)

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