integral of (sin^2(x))/(x^3)

Lösung

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

- \frac{sin ^{2} ( x )}{2 x ^{2}} - \frac{sin ( 2 x )}{2 x} + Ci (2 x) + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

= - \frac{sin ^{2} ( x )}{2 x ^{2}} - (\frac{sin ( 2 x )}{2 x} - Ci (2 x))

Vereinfache

= - \frac{sin ^{2} ( x )}{2 x ^{2}} - \frac{sin ( 2 x )}{2 x} + Ci (2 x)

Füge eine Konstante zur Lösung hinzu

= - \frac{sin ^{2} ( x )}{2 x ^{2}} - \frac{sin ( 2 x )}{2 x} + Ci (2 x) + C

\int \frac{5 x}{25 - x ^{2}} d x

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

\int \frac{( x + 2 )}{( x - 5 ) ( x + 3 )} d x

\int x^{- 1} cos (x) d x

\int sin (16 x) d x