What is the integral of sin(3x)ln(cos(3x)) ?

The integral of sin(3x)ln(cos(3x)) is 1/3 cos(3x)-1/3 cos(3x)ln(cos(3x))+C

Popular >

integral of sin(3x)ln(cos(3x))

\int sin (3 x) ln (cos (3 x)) d x

\frac{1}{3} cos (3 x) - \frac{1}{3} cos (3 x) ln (cos (3 x)) + C

Solution steps

\int sin (3 x) ln (cos (3 x)) d x

Apply Integration By Parts

: - \int sin (3 x) d x - \frac{1}{3} cos (3 x) ln (cos (3 x))

= - \int sin (3 x) d x - \frac{1}{3} cos (3 x) ln (cos (3 x))

\int sin (3 x) d x = - \frac{1}{3} cos (3 x)

= - (- \frac{1}{3} cos (3 x)) - \frac{1}{3} cos (3 x) ln (cos (3 x))

Simplify

= \frac{1}{3} cos (3 x) - \frac{1}{3} cos (3 x) ln (cos (3 x))

Add a constant to the solution

= \frac{1}{3} cos (3 x) - \frac{1}{3} cos (3 x) ln (cos (3 x)) + C

\frac{d}{d x} ((4 x^{2} + 2 x - 5) (x^{3} + 7 x + 4))

x \to 1 lim (\frac{x}{x ^{2} - x})

\frac{4 u ^{2}}{( u ^{2} + u ) ^{3}}

f (x) = a cos (2 x) + b sin (2 x)

\frac{\partial}{\partial y} (x^{3} e^{- 2 y})

What is the integral of sin(3x)ln(cos(3x)) ?
The integral of sin(3x)ln(cos(3x)) is 1/3 cos(3x)-1/3 cos(3x)ln(cos(3x))+C