integral of sin(x)+sin(x)cos(x)

Lösung

\int sin (x) + sin (x) cos (x) d x

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

Schritte zur Lösung

\int sin (x) + sin (x) cos (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 sin (x) d x + \int sin (x) cos (x) d x

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

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

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

Füge eine Konstante zur Lösung hinzu

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

d er i v a t i v e (t + e^{t}) (3 - t)

\frac{d}{d x} (\frac{2 x ^{2} - 1}{x 1 + x ^{2}})

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

d er i v a t i v e 5

\frac{d y}{d x} + 6 \cdot (tan (6 x)) \cdot y = 2 \cdot cos (6 x)