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

The integral of sin(3)(x)cos(x) is sin(3)(xsin(x)+cos(x))+C

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

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

sin (3) (x sin (x) + cos (x)) + C

Solution steps

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

Take the constant out:

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

= sin (3) \cdot \int x cos (x) d x

Apply Integration By Parts

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

= sin (3) (x sin (x) - \int sin (x) d x)

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

= sin (3) (x sin (x) - (- cos (x)))

Simplify

= sin (3) (x sin (x) + cos (x))

Add a constant to the solution

= sin (3) (x sin (x) + cos (x)) + C

x \to π lim (\frac{x}{sin ( x )})

\frac{d}{d x} (\frac{a x ^{3} + x ^{2} + 2}{1 + x + x ^{2}})

y = 5 e^{x} cos (x), (0, 5)

y = x ln^{3} (x)

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

What is the integral of sin(3)(x)cos(x) ?
The integral of sin(3)(x)cos(x) is sin(3)(xsin(x)+cos(x))+C