What is the integral of sin(x)cos(n)x ?

The integral of sin(x)cos(n)x is cos(n)(-xcos(x)+sin(x))+C

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integral of sin(x)cos(n)x

\int sin (x) cos (n) x d x

cos (n) (- x cos (x) + sin (x)) + C

Solution steps

\int sin (x) cos (n) x d x

Take the constant out:

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

= cos (n) \cdot \int sin (x) x d x

Apply Integration By Parts

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

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

= cos (n) (- x cos (x) - (- sin (x)))

Simplify

= cos (n) (- x cos (x) + sin (x))

Add a constant to the solution

= cos (n) (- x cos (x) + sin (x)) + C

y^{^{'}} = \frac{t}{1 + t ^{2}} \cdot e^{y}

\frac{d}{d r} (\frac{1}{r ^{2}})

\frac{d}{d n} ((n + 1)^{n})

d er i v a t i v e f (x) = \frac{sin ( 5 x )}{3 x}

\int \frac{1}{1 - 49 x ^{2}} d x

What is the integral of sin(x)cos(n)x ?
The integral of sin(x)cos(n)x is cos(n)(-xcos(x)+sin(x))+C