integral of (1/(sin^2(x))+2/(cos^2(x)))

Lösung

\int (\frac{1}{sin ^{2} ( x )} + \frac{2}{cos ^{2} ( x )}) d x

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

Schritte zur Lösung

\int \frac{1}{sin ^{2} ( x )} + \frac{2}{cos ^{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 \frac{1}{sin ^{2} ( x )} d x + \int \frac{2}{cos ^{2} ( x )} d x

\int \frac{1}{sin ^{2} ( x )} d x = - cot (x)

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

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

Füge eine Konstante zur Lösung hinzu

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

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

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

\int \frac{1}{( x ^{2} - 4 x + 6 ) ^{2}} d x

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

\int \frac{1}{1 - 5 x} d x