de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral from 4 to 9 of (sqrt(x))/(x-36)

Lösung

\int_{4}^{9} \frac{x}{x - 36} d x

Lösung

- 12 (\frac{1}{2} ln (\frac{3}{2}) - \frac{1}{6})

+1

Dezimale

- 0.43279 \dots

Schritte zur Lösung

\int_{4}^{9} \frac{x}{x - 36} d x

Wende U-Substitution an

= \int_{2}^{3} \frac{2 u ^{2}}{u ^{2} - 36} d u

Entferne die Konstante:

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

= 2 \cdot \int_{2}^{3} \frac{u ^{2}}{u ^{2} - 36} d u

Faktorisiere

u^{2} - 36 : - (- u^{2} + 36)

= 2 \cdot \int_{2}^{3} \frac{u ^{2}}{- ( - u ^{2} + 36 )} d u

Entferne die Konstante:

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

= 2 (- \int_{2}^{3} \frac{u ^{2}}{- u ^{2} + 36} d u)

Wende integrale Substitution an

= 2 (- \int_{\frac{1}{3}}^{\frac{1}{2}} \frac{6 v ^{2}}{- v ^{2} + 1} d v)

Entferne die Konstante:

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

= 2 (- 6 \cdot \int_{\frac{1}{3}}^{\frac{1}{2}} \frac{v ^{2}}{- v ^{2} + 1} d v)

\frac{v ^{2}}{- v ^{2} + 1} = \frac{1}{- v ^{2} + 1} - 1

= 2 (- 6 \cdot \int_{\frac{1}{3}}^{\frac{1}{2}} \frac{1}{- v ^{2} + 1} - 1 d v)

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 (- 6 (\int_{\frac{1}{3}}^{\frac{1}{2}} \frac{1}{- v ^{2} + 1} d v - \int_{\frac{1}{3}}^{\frac{1}{2}} 1 d v))

\int_{\frac{1}{3}}^{\frac{1}{2}} \frac{1}{- v ^{2} + 1} d v = \frac{ln ( \frac{3}{2} )}{2}

\int_{\frac{1}{3}}^{\frac{1}{2}} 1 d v = \frac{1}{6}

= 2 (- 6 (\frac{ln ( \frac{3}{2} )}{2} - \frac{1}{6}))

Vereinfache

2 (- 6 (\frac{ln ( \frac{3}{2} )}{2} - \frac{1}{6})) : - 12 (\frac{1}{2} ln (\frac{3}{2}) - \frac{1}{6})

= - 12 (\frac{1}{2} ln (\frac{3}{2}) - \frac{1}{6})

Graph

Beliebte Beispiele

f^'(x)=sqrt(x^2+1)

f^{^{'}} (x) = x^{2} + 1

integral of x^{-5}(x+1)

\int x^{- 5} (x + 1) d x

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

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

derivative xe^{x-1}

d er i v a t i v e x e^{x - 1}

integral of e^{sqrt(7x)}

\int e^{7 x} d x