What is the integral from 1 to 2 of 6x^24^{x^3} ?

The integral from 1 to 2 of 6x^24^{x^3} is (65532)/(ln(2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 2 of 6x^24^{x^3}

\int_{1}^{2} 6 x^{2} 4^{x^{3}} d x

\frac{65532}{ln ( 2 )}

Decimal Notation

94542.69141 \dots

Solution steps

\int_{1}^{2} 6 x^{2} \cdot 4^{x^{3}} d x

Take the constant out:

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

= 6 \cdot \int_{1}^{2} x^{2} \cdot 4^{x^{3}} d x

Apply u-substitution

: \int_{4}^{65536} \frac{u}{3 ln ( 2 ) \cdot 2 ^{\frac{l n ( u ) + l n ( 2 )}{l n ( 2 )}}} d u

= 6 \cdot \int_{4}^{65536} \frac{u}{3 ln ( 2 ) \cdot 2 ^{\frac{l n ( u ) + l n ( 2 )}{l n ( 2 )}}} d u

Take the constant out:

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

= 6 \cdot \frac{1}{3 ln ( 2 )} \cdot \int_{4}^{65536} \frac{u}{2 ^{\frac{l n ( u ) + l n ( 2 )}{l n ( 2 )}}} d u

Apply Integration By Parts

: [\frac{u ^{2}}{2 ^{\frac{l n ( 2 u ) + l n ( 2 )}{l n ( 2 )}}} - \int - \frac{1}{4} d u]_{4}^{65536}

= 6 \cdot \frac{1}{3 ln ( 2 )} [\frac{u ^{2}}{2 ^{\frac{l n ( 2 u ) + l n ( 2 )}{l n ( 2 )}}} - \int - \frac{1}{4} d u]_{4}^{65536}

\int - \frac{1}{4} d u = - \frac{1}{4} u

= 6 \cdot \frac{1}{3 ln ( 2 )} [\frac{u ^{2}}{2 ^{\frac{l n ( 2 u ) + l n ( 2 )}{l n ( 2 )}}} - (- \frac{1}{4} u)]_{4}^{65536}

Simplify

6 \cdot \frac{1}{3 ln ( 2 )} [\frac{u ^{2}}{2 ^{\frac{l n ( 2 u ) + l n ( 2 )}{l n ( 2 )}}} - (- \frac{1}{4} u)]_{4}^{65536} : \frac{2}{ln ( 2 )} [\frac{u ^{2}}{2 ^{\frac{l n ( 2 u ) + l n ( 2 )}{l n ( 2 )}}} + \frac{1}{4} u]_{4}^{65536}

= \frac{2}{ln ( 2 )} [\frac{u ^{2}}{2 ^{\frac{l n ( 2 u ) + l n ( 2 )}{l n ( 2 )}}} + \frac{1}{4} u]_{4}^{65536}

Compute the boundaries:

32766

= \frac{2}{ln ( 2 )} \cdot 32766

Simplify

= \frac{65532}{ln ( 2 )}

x \to 3 lim (\frac{x - 3}{∣ x - 3 ∣})

\int \frac{4 x ^{2} + 2}{( x ^{2} - 2 x + 2 ) ^{2}} d x

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

y = 7 - x^{2}

y = (1 - x) (x^{2} - 8)^{2}, (3, - 2)

What is the integral from 1 to 2 of 6x^24^{x^3} ?
The integral from 1 to 2 of 6x^24^{x^3} is (65532)/(ln(2))