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

Lösung

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

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

Schritte zur Lösung

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

l a pl a ce t r an s f or m e^{m t}

\int \frac{x}{5 + 4 x} d x

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

\frac{d}{d x} (3 x^{5} - 4 x^{4} + 9 x - 6)

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