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Beliebt Rechnen >

integral from 2 to 5 of x/(sqrt(x-1))

Lösung

\int_{2}^{5} \frac{x}{x - 1} d x

Lösung

\frac{20}{3}

+1

Dezimale

6.66666 \dots

Schritte zur Lösung

\int_{2}^{5} \frac{x}{x - 1} d x

Wende U-Substitution an

= \int_{1}^{2} 2 (u^{2} + 1) d u

Entferne die Konstante:

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

= 2 \cdot \int_{1}^{2} u^{2} + 1 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_{1}^{2} u^{2} d u + \int_{1}^{2} 1 d u)

\int_{1}^{2} u^{2} d u = \frac{7}{3}

\int_{1}^{2} 1 d u = 1

= 2 (\frac{7}{3} + 1)

Vereinfache

2 (\frac{7}{3} + 1) : \frac{20}{3}

= \frac{20}{3}

Graph

Beliebte Beispiele

derivative of 1/(4x^2+1)

\frac{d}{d x} (\frac{1}{4 x ^{2} + 1})

(\partial)/(\partial x)(((2x+3y))/(4x+5y))

\frac{\partial}{\partial x} (\frac{( 2 x + 3 y )}{4 x + 5 y})

f(x)=sqrt(x^2+5)

f (x) = x^{2} + 5

taylor cos(pix),1

t a y l or cos (π x), 1

integral from 0 to 1 of (x^4+1)/x

\int_{0}^{1} \frac{x ^{4} + 1}{x} d x