integral of (3/(1+x^2)-2/(sqrt(1-x^2)))

Lösung

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

3 arctan (x) - 2 arcsin (x) + C

Schritte zur Lösung

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

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

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

= 3 arctan (x) - 2 arcsin (x)

Füge eine Konstante zur Lösung hinzu

= 3 arctan (x) - 2 arcsin (x) + C

\int \frac{x + 3}{x ^{2} - 5 x + 6} d x

\int cos (2 x) sin (5 x) d x

\int x^{2} 3 x d x

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

\int y cos (5 y) d y