de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral from 9 to 25 of (sqrt(x-9))/x

Lösung

\int_{9}^{25} \frac{x - 9}{x} d x

Lösung

6 (- arctan (\frac{4}{3}) + \frac{4}{3})

+1

Dezimale

2.43622 \dots

Schritte zur Lösung

\int_{9}^{25} \frac{x - 9}{x} d x

Wende U-Substitution an

= \int_{0}^{4} \frac{2 u ^{2}}{u ^{2} + 9} d u

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{4} \frac{u ^{2}}{u ^{2} + 9} d u

\frac{u ^{2}}{u ^{2} + 9} = - \frac{9}{u ^{2} + 9} + 1

= 2 \cdot \int_{0}^{4} - \frac{9}{u ^{2} + 9} + 1 d u

Wende integrale Substitution an

= 2 \cdot \int_{0}^{\frac{4}{3}} 3 (- \frac{1}{v ^{2} + 1} + 1) d v

Entferne die Konstante:

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

= 2 \cdot 3 \cdot \int_{0}^{\frac{4}{3}} - \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 \cdot 3 (- \int_{0}^{\frac{4}{3}} \frac{1}{v ^{2} + 1} d v + \int_{0}^{\frac{4}{3}} 1 d v)

\int_{0}^{\frac{4}{3}} \frac{1}{v ^{2} + 1} d v = arctan (\frac{4}{3})

\int_{0}^{\frac{4}{3}} 1 d v = \frac{4}{3}

= 2 \cdot 3 (- arctan (\frac{4}{3}) + \frac{4}{3})

Vereinfache

= 6 (- arctan (\frac{4}{3}) + \frac{4}{3})

Graph

Beliebte Beispiele

(cos(x)+ysin(x))dx+(cos(x))dy=0

(cos (x) + y sin (x)) d x + (cos (x)) d y = 0

(\partial)/(\partial x)(6xye^{-x^2-y^2})

\frac{\partial}{\partial x} (6 x y e^{- x^{2} - y^{2}})

tangent y=6sec(x),\at x= pi/6

t an g e n t y = 6 sec (x), at x = \frac{π}{6}

integral of cos^4(x

\int cos^{4} (d) x d x

x^2y^{''}+3xy^'+3y=0

x^{2} y^{^{''}} + 3 x y^{^{'}} + 3 y = 0