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Beliebt Rechnen >

integral from 0 to 15 of w/((1+w)^{3/4)}

Lösung

\int_{0}^{15} \frac{w}{( 1 + w ) ^{\frac{3}{4}}} d w

Lösung

\frac{104}{5}

+1

Dezimale

20.8

Schritte zur Lösung

\int_{0}^{15} \frac{w}{( 1 + w ) ^{\frac{3}{4}}} d w

Wende U-Substitution an

= \int_{1}^{16} \frac{u - 1}{u ^{\frac{3}{4}}} d u

Multipliziere aus

\frac{u - 1}{u ^{\frac{3}{4}}} : u^{\frac{1}{4}} - \frac{1}{u ^{\frac{3}{4}}}

= \int_{1}^{16} u^{\frac{1}{4}} - \frac{1}{u ^{\frac{3}{4}}} 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

= \int_{1}^{16} u^{\frac{1}{4}} d u - \int_{1}^{16} \frac{1}{u ^{\frac{3}{4}}} d u

\int_{1}^{16} u^{\frac{1}{4}} d u = \frac{124}{5}

\int_{1}^{16} \frac{1}{u ^{\frac{3}{4}}} d u = 4

= \frac{124}{5} - 4

Vereinfache

\frac{124}{5} - 4 : \frac{104}{5}

= \frac{104}{5}

Graph

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integral of x/(4+5x^2)

\int \frac{x}{4 + 5 x ^{2}} d x

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