What is the integral from 0 to 1 of x^22^{x^3} ?

The integral from 0 to 1 of x^22^{x^3} is 1/(3ln(2))

Popular >

integral from 0 to 1 of x^22^{x^3}

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

\frac{1}{3 ln ( 2 )}

Decimal

0.48089 \dots

Solution steps

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

Apply u-substitution

: \int_{0}^{1} \frac{2 ^{u}}{3} d u

= \int_{0}^{1} \frac{2 ^{u}}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int_{0}^{1} 2^{u} d u

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

= \frac{1}{3} [\frac{2 ^{u}}{ln ( 2 )}]_{0}^{1}

Compute the boundaries:

\frac{1}{ln ( 2 )}

= \frac{1}{3} \cdot \frac{1}{ln ( 2 )}

Simplify

= \frac{1}{3 ln ( 2 )}

\int_{1}^{e} ln (x^{3}) d x

\int_{- 4}^{4} - ∣ x ∣ + 4 d x

\int_{3}^{5} (2 x + 9) d x

\int_{8}^{11} 2 x + 3 d x

\int_{0}^{5} \frac{2}{3 x + 2} d x

What is the integral from 0 to 1 of x^22^{x^3} ?
The integral from 0 to 1 of x^22^{x^3} is 1/(3ln(2))