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

The integral of 2x-1/(e^{x^2)} is x^2-(sqrt(pi))/2 \erf(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2x-1/(e^{x^2)}

\int 2 x - \frac{1}{e ^{x^{2}}} d x

x^{2} - \frac{π}{2} erf (x) + C

Solution steps

\int 2 x - \frac{1}{e ^{x^{2}}} d x

Apply exponent rule:

\frac{1}{a ^{b}} = a^{- b}

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

= \int 2 x - e^{- x^{2}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 x d x - \int e^{- x^{2}} d x

\int 2 x d x = x^{2}

\int e^{- x^{2}} d x = \frac{π}{2} erf (x)

= x^{2} - \frac{π}{2} erf (x)

Add a constant to the solution

= x^{2} - \frac{π}{2} erf (x) + C

14 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)

(x + 7) \cdot ln (x)

\frac{1}{ln ( x )}

x \to 3 lim (4 - x^{2})

\frac{d}{d x} (2 x + \frac{8}{x})

What is the integral of 2x-1/(e^{x^2)} ?
The integral of 2x-1/(e^{x^2)} is x^2-(sqrt(pi))/2 \erf(x)+C