integral of cos(x)ln(x)sin(x)

Lösung

\int cos (x) ln (x) sin (x) d x

\frac{1}{2} sin^{2} (x) ln (x) - \frac{1}{4} (ln ∣ x ∣ - Ci (2 x)) + C

Schritte zur Lösung

\int cos (x) ln (x) sin (x) d x

Wende die partielle Integration an

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

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

= \frac{1}{2} sin^{2} (x) ln (x) - \frac{1}{4} (ln ∣ x ∣ - Ci (2 x))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} sin^{2} (x) ln (x) - \frac{1}{4} (ln ∣ x ∣ - Ci (2 x)) + C

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

n = 0 \sum \infty \frac{5}{n + 2}

d er i v a t i v e y = x^{4}

y^{^{''}} + 4 y^{^{'}} + 5 y = - 5 x + e^{- x}

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