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

Lösung

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int (x^{3} + 2 x^{2} + x - 1) e^{- 5 x} d x

in t e g r a l \frac{x ^{3}}{3}

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

\int \frac{( x ^{2} + x )}{( 4 - 3 x ^{2} - 2 x ^{3} ) ^{4}} d x

\int \frac{ln ( 8 x )}{3 x ^{2}} d x