What is the integral of x2^{x^2} ?

The integral of x2^{x^2} is (2^{x^2-1})/(ln(2))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x2^{x^2}

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

\frac{2 ^{x^{2} - 1}}{ln ( 2 )} + C

Solution steps

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

Apply u-substitution

: \int 2^{u - 1} d u

= \int 2^{u - 1} d u

Simplify

2^{u - 1} : 2^{u} \cdot 2^{- 1}

= \int 2^{u} \cdot 2^{- 1} d u

Take the constant out:

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

= 2^{- 1} \cdot \int 2^{u} d u

Apply exponent rule:

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

= \frac{1}{2} \cdot \int 2^{u} d u

\int a^{x} d x = \frac{a ^{x}}{ln a}

= \frac{1}{2} \cdot \frac{2 ^{u}}{ln ( 2 )}

Substitute back

u = x^{2}

= \frac{1}{2} \cdot \frac{2 ^{x^{2}}}{ln ( 2 )}

Simplify

\frac{1}{2} \cdot \frac{2 ^{x^{2}}}{ln ( 2 )} : \frac{2 ^{x^{2} - 1}}{ln ( 2 )}

= \frac{2 ^{x^{2} - 1}}{ln ( 2 )}

Add a constant to the solution

= \frac{2 ^{x^{2} - 1}}{ln ( 2 )} + C

\int + \frac{x}{x ^{4} + 7} d x

\frac{d}{d x} (\frac{3}{1 - 2 x})

\int_{0}^{\frac{1}{2}} 8 arccos (x) d x

x \to 0 lim (- ln (x))

\int - 6 d x

What is the integral of x2^{x^2} ?
The integral of x2^{x^2} is (2^{x^2-1})/(ln(2))+C