What is the integral of cos^2(x)ln(x) ?

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

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integral of cos^2(x)ln(x)

\int cos^{2} (x) ln (x) d x

\frac{1}{2} ln (x) (x + \frac{1}{2} sin (2 x)) - \frac{1}{4} (2 x + Si (2 x)) + C

Solution steps

\int cos^{2} (x) ln (x) d x

Apply Integration By Parts

: \frac{1}{2} ln (x) (x + \frac{1}{2} sin (2 x)) - \int \frac{2 x + sin ( 2 x )}{4 x} d x

= \frac{1}{2} ln (x) (x + \frac{1}{2} sin (2 x)) - \int \frac{2 x + sin ( 2 x )}{4 x} d x

\int \frac{2 x + sin ( 2 x )}{4 x} d x = \frac{1}{4} (2 x + Si (2 x))

= \frac{1}{2} ln (x) (x + \frac{1}{2} sin (2 x)) - \frac{1}{4} (2 x + Si (2 x))

Add a constant to the solution

= \frac{1}{2} ln (x) (x + \frac{1}{2} sin (2 x)) - \frac{1}{4} (2 x + Si (2 x)) + C

f (x) = (1 + x + x^{2})^{99}

\int 1 - cos^{2} (x) d x

\int \frac{1}{x ^{1.5}} d x

f (x) = 2 cos (sin (x))

\frac{d y}{d t} - \frac{7}{t} y = t^{5}

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