integral of 5sin(3x)-4xsec(x^2)

Lösung

\int 5 sin (3 x) - 4 x sec (x^{2}) d x

- \frac{5}{3} cos (3 x) - 2 ln tan (x^{2}) + sec (x^{2}) + C

Schritte zur Lösung

\int 5 sin (3 x) - 4 x sec (x^{2}) 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 5 sin (3 x) d x - \int 4 x sec (x^{2}) d x

\int 5 sin (3 x) d x = - \frac{5}{3} cos (3 x)

\int 4 x sec (x^{2}) d x = 2 ln tan (x^{2}) + sec (x^{2})

= - \frac{5}{3} cos (3 x) - 2 ln tan (x^{2}) + sec (x^{2})

Füge eine Konstante zur Lösung hinzu

= - \frac{5}{3} cos (3 x) - 2 ln tan (x^{2}) + sec (x^{2}) + C

\int \frac{x ^{2} + 1}{x ^{3} + 4 x ^{2} + 3 x} d x

\int w^{3} sin (w) d w

\int tan^{3} (3 x) sec^{6} (3 x) d x

\int \frac{1}{x 6 x - 1} d x

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