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

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

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integral of-cos(x)ln(x)

\int - cos (x) ln (x) d x

- ln (x) sin (x) + Si (x) + C

Solution steps

\int - cos (x) ln (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int cos (x) ln (x) d x

Apply Integration By Parts

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

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

\int \frac{sin ( x )}{x} d x = Si (x)

= - (ln (x) sin (x) - Si (x))

Simplify

= - ln (x) sin (x) + Si (x)

Add a constant to the solution

= - ln (x) sin (x) + Si (x) + C

\int \frac{x}{( 36 - x ^{2} ) ^{3}} d x

x \to \infty lim (1 + x^{2})

(e^{s i n (x)})^{^{'}}

\int_{1}^{4} e^{x} d x

y = (x^{2} + 1)^{5} (1 - x^{2})^{5}

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