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Beliebt Rechnen >

integral of sin(x)(3cos(x)-1)

Lösung

\int sin (x) (3 cos (x) - 1) d x

Lösung

\frac{3}{2} sin^{2} (x) + cos (x) + C

Schritte zur Lösung

\int sin (x) (3 cos (x) - 1) d x

Multipliziere aus

sin (x) (3 cos (x) - 1) : 3 sin (x) cos (x) - sin (x)

= \int 3 sin (x) cos (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 3 sin (x) cos (x) d x - \int sin (x) d x

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

\int sin (x) d x = - cos (x)

= \frac{3}{2} sin^{2} (x) - (- cos (x))

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

= \frac{3}{2} sin^{2} (x) + cos (x) + C

Graph

Beliebte Beispiele

integral of (3x^2+x)/((8x^3+4x^2)^2)

\int \frac{3 x ^{2} + x}{( 8 x ^{3} + 4 x ^{2} ) ^{2}} d x

integral of (2sqrt(x)-6)

\int (2 x - 6) d x

integral of 4xy+3x^2

\int 4 x y + 3 x^{2} d x

integral of x^2(x^3+4)^2

\int x^{2} (x^{3} + 4)^{2} d x

integral of (x^4-8)/(x^2)

\int \frac{x ^{4} - 8}{x ^{2}} d x