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Beliebt Rechnen >

integral of ((x+1)/(sqrt(x-1)))

Lösung

\int (\frac{x + 1}{x - 1}) d x

Lösung

2 (\frac{1}{3} (x - 1)^{\frac{3}{2}} + 2 x - 1) + C

Schritte zur Lösung

\int \frac{x + 1}{x - 1} d x

Wende U-Substitution an

= \int 2 (u^{2} + 2) d u

Entferne die Konstante:

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

= 2 \cdot \int u^{2} + 2 d u

Wende die Summenregel an:

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

= 2 (\int u^{2} d u + \int 2 d u)

\int u^{2} d u = \frac{u ^{3}}{3}

\int 2 d u = 2 u

= 2 (\frac{u ^{3}}{3} + 2 u)

Setze in

u = x - 1

ein

= 2 (\frac{( x - 1 ) ^{3}}{3} + 2 x - 1)

Vereinfache

2 (\frac{( x - 1 ) ^{3}}{3} + 2 x - 1) : 2 (\frac{1}{3} (x - 1)^{\frac{3}{2}} + 2 x - 1)

= 2 (\frac{1}{3} (x - 1)^{\frac{3}{2}} + 2 x - 1)

Füge eine Konstante zur Lösung hinzu

= 2 (\frac{1}{3} (x - 1)^{\frac{3}{2}} + 2 x - 1) + C

Graph

Beliebte Beispiele

tangent f(x)=e^x,\at x=ln(13)

t an g e n t f (x) = e^{x}, at x = ln (13)

tangent f(x)=e^x(8+3x+5x^2),\at x=0

t an g e n t f (x) = e^{x} (8 + 3 x + 5 x^{2}), at x = 0

derivative of x^3e^{-4x}

\frac{d}{d x} (x^{3} e^{- 4 x})

(dy)/(dx)+y-4cos(x)=0

\frac{d y}{d x} + y - 4 cos (x) = 0

integral from 0 to 5 of 1/(x^{17/18)}

\int_{0}^{5} \frac{1}{x ^{\frac{17}{18}}} d x