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

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

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

\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

Solution steps

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

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

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

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

y = x^{4}

33.62 x^{^{'}} + x = 100

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