de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral from 1 to sqrt(2 of)x8^{x^2}

Lösung

\int_{1}^{2} x 8^{x^{2}} d x

Lösung

\frac{28}{3 ln ( 2 )}

+1

Dezimale

13.46515 \dots

Schritte zur Lösung

\int_{1}^{2} x \cdot 8^{x^{2}} d x

Wende U-Substitution an

= \int_{8}^{64} \frac{u}{3 ln ( 2 ) \cdot 2 ^{\frac{l n ( u ) + l n ( 2 )}{l n ( 2 )}}} d u

Entferne die Konstante:

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

= \frac{1}{3 ln ( 2 )} \cdot \int_{8}^{64} \frac{u}{2 ^{\frac{l n ( u ) + l n ( 2 )}{l n ( 2 )}}} d u

Wende die partielle Integration an

= \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]_{8}^{64}

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

= \frac{1}{3 ln ( 2 )} [\frac{u ^{2}}{2 ^{\frac{l n ( 2 u ) + l n ( 2 )}{l n ( 2 )}}} - (- \frac{1}{4} u)]_{8}^{64}

Vereinfache

= \frac{1}{3 ln ( 2 )} [\frac{u ^{2}}{2 ^{\frac{l n ( 2 u ) + l n ( 2 )}{l n ( 2 )}}} + \frac{1}{4} u]_{8}^{64}

Berechne die Grenzen:

28

= \frac{1}{3 ln ( 2 )} \cdot 28

Vereinfache

= \frac{28}{3 ln ( 2 )}

Graph

Beliebte Beispiele

y^'=(y(x-y))/(x^2)

y^{^{'}} = \frac{y ( x - y )}{x ^{2}}

\frac{d y}{d x} = 2 + 3 y

limit as x approaches 0 of ln(x^2)(-2)

x \to 0 lim (ln (x^{2}) (- 2))

(\partial)/(\partial x)(x^2+3xy^2+2y)

\frac{\partial}{\partial x} (x^{2} + 3 x y^{2} + 2 y)

y^{''}+4y=2cos(2t)

y^{^{''}} + 4 y = 2 cos (2 t)