What is the integral of e^{sqrt(t)} ?

The integral of e^{sqrt(t)} is 2(e^{sqrt(t)}sqrt(t)-e^{sqrt(t)})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{sqrt(t)}

\int e^{t} d t

2 (e^{t} t - e^{t}) + C

Solution steps

\int e^{t} d t

Apply u-substitution

: \int e^{u} \cdot 2 u d u

= \int e^{u} \cdot 2 u d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int e^{u} u d u

Apply Integration By Parts

: e^{u} u - \int e^{u} d u

= 2 (e^{u} u - \int e^{u} d u)

\int e^{u} d u = e^{u}

= 2 (e^{u} u - e^{u})

Substitute back

u = t

= 2 (e^{t} t - e^{t})

Add a constant to the solution

= 2 (e^{t} t - e^{t}) + C

\int \frac{3}{9 - 4 x ^{2}} d x

\int tan^{3} (x) sec^{11} (x) d x

\int \frac{x ^{2}}{x ^{3} + 5} d x

\int x^{- 3} arctan (x) d x

\int \frac{sin ^{2} ( x )}{1 + sin ^{2} ( x )} d x

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