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

The integral of sin(x)ln(c)osx is osln(c)(-xcos(x)+sin(x))+C

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integral of sin(x)ln(c)osx

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

os ln (c) (- x cos (x) + sin (x)) + C

Solution steps

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

Take the constant out:

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

= ln (c) os \cdot \int sin (x) x d x

Apply Integration By Parts

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

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

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

= ln (c) os (- x cos (x) - (- sin (x)))

Simplify

= os ln (c) (- x cos (x) + sin (x))

Add a constant to the solution

= os ln (c) (- x cos (x) + sin (x)) + C

sin (2 t) sin (5 t)

\frac{\partial}{\partial x} (y x + 2 x)

\int \frac{1 + sin ( x )}{1 - sin ( x )} d x

\int x ln (x + 2) d x

\int_{0}^{1} 2 π x e^{- x^{2}} d x

What is the integral of sin(x)ln(c)osx ?
The integral of sin(x)ln(c)osx is osln(c)(-xcos(x)+sin(x))+C