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) \cdot 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

f (x) = arcsin (2 x - 3)

\frac{d}{d x} (6 tan^{2} (3 x))

\int \frac{6 x ^{2} + x + 7}{( x + 1 ) ( x ^{2} + 1 )} d x

\frac{d y}{d x} = \frac{y}{x} + 4 x + 9

\frac{d y}{d x} + 3 y = 2 x e^{- 3 x}

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