integral of (sqrt(x))/((4x+9)^2)

Lösung

\int \frac{x}{( 4 x + 9 ) ^{2}} d x

- \frac{x}{4 ( 4 x + 9 )} + \frac{1}{24} arctan (\frac{2}{3} x) + C

Schritte zur Lösung

\int \frac{x}{( 4 x + 9 ) ^{2}} d x

Wende die partielle Integration an

= - \frac{x}{4 ( 4 x + 9 )} - \int - \frac{1}{8 x ( 4 x + 9 )} d x

\int - \frac{1}{8 x ( 4 x + 9 )} d x = - \frac{1}{24} arctan (\frac{2}{3} x)

= - \frac{x}{4 ( 4 x + 9 )} - (- \frac{1}{24} arctan (\frac{2}{3} x))

Vereinfache

= - \frac{x}{4 ( 4 x + 9 )} + \frac{1}{24} arctan (\frac{2}{3} x)

Füge eine Konstante zur Lösung hinzu

= - \frac{x}{4 ( 4 x + 9 )} + \frac{1}{24} arctan (\frac{2}{3} x) + C

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

\int cosh (2 x) sinh^{2} (2 x) d x

\int 5 sec^{2} (x) e^{t a n (x)} d x

\int x e^{- c x} d x

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