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

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

Popular >

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

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

y^{^{'}} = \frac{( 1 - 2 t )}{y}

\int_{0}^{4} (4 x^{2} + 7 x) d x

\frac{d}{d x} (e^{x} x^{3})

\frac{d y}{d x} = (\frac{( 2 y + 7 )}{( 8 x + 9 )})^{2}

\frac{s ( s + 2 )}{( s + 1 ) ^{2}}

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