integral of (xcos^2(y)-sin(y))

Lösung

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

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

Schritte zur Lösung

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

\int sin (y) d x = sin (y) x

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

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

Füge eine Konstante zur Lösung hinzu

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

\int [cos (\frac{x}{2}) - sin (3 \frac{x}{2})] d x

\frac{d}{d x} (\frac{7}{x ^{- 2}} + \frac{5}{x ^{- 3}})

a re a x, \frac{1}{3} x, x = 25

x \to 0 lim (\frac{100}{2})

\frac{d}{d x} (tan^{4} (3) x^{2})