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

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

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integral of sin(x)sin(n)x

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

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

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

n = 1 \sum \infty \frac{4}{n ( n + 6 )}

\int sin^{4} (x) cos^{3} (x) d x

\int \frac{y ^{2} + 1}{( y - 1 ) ^{2} ( y + 1 )} d y

y^{^{''}} + 2 y^{^{'}} + 4 y = e^{t} cos (t)

\frac{\partial}{\partial z} (y sin (x z))

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