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

The integral of ln(x)sin(x) is -ln(x)cos(x)+\Ci(x)+C

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integral of ln(x)sin(x)

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

- ln (x) cos (x) + Ci (x) + C

Solution steps

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

Apply Integration By Parts

: - ln (x) cos (x) - \int - \frac{cos ( x )}{x} d x

= - ln (x) cos (x) - \int - \frac{cos ( x )}{x} d x

\int - \frac{cos ( x )}{x} d x = - Ci (x)

= - ln (x) cos (x) - (- Ci (x))

Simplify

= - ln (x) cos (x) + Ci (x)

Add a constant to the solution

= - ln (x) cos (x) + Ci (x) + C

\int \frac{2}{x} - \frac{1}{x ^{2}} d x

\int \frac{2 x}{4 x - 5} d x

\frac{d r}{d t} = \frac{r ^{2}}{t}

(- 3 x + 2)^{2}

\frac{d}{d x} (5^{3 x} + 7)

What is the integral of ln(x)sin(x) ?
The integral of ln(x)sin(x) is -ln(x)cos(x)+\Ci(x)+C