What is the integral from 0 to 1 of x3^{x^2} ?

The integral from 0 to 1 of x3^{x^2} is 1/(ln(3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 1 of x3^{x^2}

\int_{0}^{1} x 3^{x^{2}} d x

\frac{1}{ln ( 3 )}

Decimal

0.91023 \dots

Solution steps

\int_{0}^{1} x \cdot 3^{x^{2}} d x

Apply u-substitution

: \int_{1}^{3} \frac{1}{2 ln ( 3 )} d u

= \int_{1}^{3} \frac{1}{2 ln ( 3 )} d u

Integral of a constant:

\int a d x = a x

= [\frac{1}{2 ln ( 3 )} u]_{1}^{3}

Compute the boundaries:

\frac{1}{ln ( 3 )}

= \frac{1}{ln ( 3 )}

\int_{- 2}^{0} \frac{1}{1 - x} d x

\int_{- π}^{π} e^{- x} d x

\int_{- π}^{π} t^{2} cos (t) d t

\int_{- 2}^{2} (x + 2) d x

\int_{0}^{\frac{1}{3}} \frac{1}{81 x ^{2} + 9} d x

What is the integral from 0 to 1 of x3^{x^2} ?
The integral from 0 to 1 of x3^{x^2} is 1/(ln(3))