integral of sin(x)(2x^2+cos^3(x))

Lösung

\int sin (x) (2 x^{2} + cos^{3} (x)) d x

2 (- x^{2} cos (x) + 2 (x sin (x) + cos (x))) - \frac{cos ^{4} ( x )}{4} + C

Schritte zur Lösung

\int sin (x) (2 x^{2} + cos^{3} (x)) d x

Multipliziere aus

sin (x) (2 x^{2} + cos^{3} (x)) : 2 x^{2} sin (x) + cos^{3} (x) sin (x)

= \int 2 x^{2} sin (x) + cos^{3} (x) sin (x) d x

Wende die Summenregel an:

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

= \int 2 x^{2} sin (x) d x + \int cos^{3} (x) sin (x) d x

\int 2 x^{2} sin (x) d x = 2 (- x^{2} cos (x) + 2 (x sin (x) + cos (x)))

\int cos^{3} (x) sin (x) d x = - \frac{cos ^{4} ( x )}{4}

= 2 (- x^{2} cos (x) + 2 (x sin (x) + cos (x))) - \frac{cos ^{4} ( x )}{4}

Füge eine Konstante zur Lösung hinzu

= 2 (- x^{2} cos (x) + 2 (x sin (x) + cos (x))) - \frac{cos ^{4} ( x )}{4} + C

\int \frac{csc ( x ) cot ( x )}{4} d x

\int sin (x) \cdot x^{2} d x

\int \frac{8}{x x ^{2} - 1} d x

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