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

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

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integral of sin(x)ln(x)

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

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

Solution steps

\int sin (x) ln (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) = \frac{9}{t}

\frac{d y}{d x}, 25 x^{2} - 10 x y + 4 y^{2} = 100

\int \frac{( x ^{3} )}{9 - x ^{2}} d x

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

h (x) = \frac{( 3 x - 5 )}{1 - x ^{2}}

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