integral from-5 to 2 of x/((x+6)^{2/3)}

Lösung

\int_{- 5}^{2} \frac{x}{( x + 6 ) ^{\frac{2}{3}}} d x

- \frac{27}{4}

Dezimale

- 6.75

Schritte zur Lösung

\int_{- 5}^{2} \frac{x}{( x + 6 ) ^{\frac{2}{3}}} d x

Wende U-Substitution an

= \int_{1}^{8} \frac{u - 6}{u ^{\frac{2}{3}}} d u

Multipliziere aus

\frac{u - 6}{u ^{\frac{2}{3}}} : u^{\frac{1}{3}} - \frac{6}{u ^{\frac{2}{3}}}

= \int_{1}^{8} u^{\frac{1}{3}} - \frac{6}{u ^{\frac{2}{3}}} 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}^{8} u^{\frac{1}{3}} d u - \int_{1}^{8} \frac{6}{u ^{\frac{2}{3}}} d u

\int_{1}^{8} u^{\frac{1}{3}} d u = \frac{45}{4}

\int_{1}^{8} \frac{6}{u ^{\frac{2}{3}}} d u = 18

= \frac{45}{4} - 18

Vereinfache

\frac{45}{4} - 18 : - \frac{27}{4}

= - \frac{27}{4}

\int_{1}^{\infty} ln (x^{2}) d x

\int_{1}^{5} (x + 2) d x

\int_{0}^{2} z^{2} ln (z) d z

\int_{0}^{2} 6 x^{2} - 3 x^{3} d x

\int_{0}^{8} 1000 x + 250 d x