What is the integral of sin(x)ln(x)cos(x) ?

The integral of sin(x)ln(x)cos(x) is 1/2 sin^2(x)ln(x)-1/4 (ln|x|-\Ci(2x))+C

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

\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

Solution steps

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

Apply Integration By Parts

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

= \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))

Add a constant to the solution

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

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

What is the integral of sin(x)ln(x)cos(x) ?
The integral of sin(x)ln(x)cos(x) is 1/2 sin^2(x)ln(x)-1/4 (ln|x|-\Ci(2x))+C