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Beliebt Rechnen >

integral of x^2arctan(2x^3)

Lösung

\int x^{2} arctan (2 x^{3}) d x

Lösung

\frac{1}{3} x^{3} arctan (2 x^{3}) - \frac{1}{12} ln 4 x^{6} + 1 + C

Schritte zur Lösung

\int x^{2} arctan (2 x^{3}) d x

Wende die partielle Integration an

= \frac{1}{3} x^{3} arctan (2 x^{3}) - \int \frac{2 x ^{5}}{4 x ^{6} + 1} d x

\int \frac{2 x ^{5}}{4 x ^{6} + 1} d x = \frac{1}{12} ln 4 x^{6} + 1

= \frac{1}{3} x^{3} arctan (2 x^{3}) - \frac{1}{12} ln 4 x^{6} + 1

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} x^{3} arctan (2 x^{3}) - \frac{1}{12} ln 4 x^{6} + 1 + C

Graph

Beliebte Beispiele

integral of 1/(xsqrt(x^2+36))

\int \frac{1}{x x ^{2} + 36} d x

integral of 1/(uln(u))

\int \frac{1}{u ln ( u )} d u

integral of 3^{t^2}

\int 3^{t^{2}} d t

derivative of (3+2x/(sqrt(x)))

\frac{d}{d x} (\frac{3 + 2 x}{x})

(d^3)/(dx^3)(sqrt(6t+3))

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