integral of cos(x)sqrt(4-3sin(x))

Lösung

\int cos (x) 4 - 3 sin (x) d x

sin (x) 4 - 3 sin (x) + \frac{1}{9} ((- 3 sin (x) + 4)^{\frac{3}{2}} - 12 - 3 sin (x) + 4) + C

Schritte zur Lösung

\int cos (x) 4 - 3 sin (x) d x

Wende die partielle Integration an

= sin (x) 4 - 3 sin (x) - \int - \frac{3 cos ( x ) sin ( x )}{2 4 - 3 sin ( x )} d x

\int - \frac{3 cos ( x ) sin ( x )}{2 4 - 3 sin ( x )} d x = - \frac{1}{9} ((- 3 sin (x) + 4)^{\frac{3}{2}} - 12 - 3 sin (x) + 4)

= sin (x) 4 - 3 sin (x) - (- \frac{1}{9} ((- 3 sin (x) + 4)^{\frac{3}{2}} - 12 - 3 sin (x) + 4))

Vereinfache

= sin (x) 4 - 3 sin (x) + \frac{1}{9} ((- 3 sin (x) + 4)^{\frac{3}{2}} - 12 - 3 sin (x) + 4)

Füge eine Konstante zur Lösung hinzu

= sin (x) 4 - 3 sin (x) + \frac{1}{9} ((- 3 sin (x) + 4)^{\frac{3}{2}} - 12 - 3 sin (x) + 4) + C

\frac{d}{d x} (f (x) (g (x) (2 x)))

\int ln (x + (x^{2} + 1)) d x

x \to 1 lim (\frac{x ^{2} - 4}{x - 2})

d er i v a t i v e 4 (5 - 9 x)^{5}

\int (\frac{6}{x} + \frac{x}{6}) d x