integral of (tan^2(x)+cot^2(x))

Lösung

\int (tan^{2} (x) + cot^{2} (x)) d x

- 2 x + tan (x) - cot (x) + C

Schritte zur Lösung

\int tan^{2} (x) + cot^{2} (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 tan^{2} (x) d x + \int cot^{2} (x) d x

\int tan^{2} (x) d x = - x + tan (x)

\int cot^{2} (x) d x = - x - cot (x)

= - x + tan (x) - x - cot (x)

Vereinfache

= - 2 x + tan (x) - cot (x)

Füge eine Konstante zur Lösung hinzu

= - 2 x + tan (x) - cot (x) + C

\int sin (\frac{3}{2}) θ cos (\frac{3}{2}) θ d θ

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

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

\int \frac{2 sec ( x )}{2 tan ( x ) + 3 sec ( x )} d x

\int \frac{e ^{x} e ^{x} + 2}{e ^{x} + 4} d x