integral of 7xarcsin(x)

Lösung

\int 7 x arcsin (x) d x

7 (\frac{1}{2} x^{2} arcsin (x) - \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x)))) + C

Schritte zur Lösung

\int 7 x arcsin (x) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 7 \cdot \int x arcsin (x) d x

Wende die partielle Integration an

= 7 (\frac{1}{2} x^{2} arcsin (x) - \int \frac{x ^{2}}{2 1 - x ^{2}} d x)

\int \frac{x ^{2}}{2 1 - x ^{2}} d x = \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x)))

= 7 (\frac{1}{2} x^{2} arcsin (x) - \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x))))

Füge eine Konstante zur Lösung hinzu

= 7 (\frac{1}{2} x^{2} arcsin (x) - \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x)))) + C

x \to 0 lim (\frac{9}{x} - \frac{9}{∣ x ∣})

\int \frac{( sin ( ln ( x ) ) )}{x} d x

4 y^{^{''}} + 4 y^{^{'}} - 3 y = cos (2 x)

\int_{2}^{3} \frac{26}{3 - x} d x

d er i v a t i v e f (x) = \frac{e ^{x}}{8 x ^{2} + 3}