What is the integral of sin(n)x ?

The integral of sin(n)x is 1/2 x^2sin(n)+C

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integral of sin(n)x

\int sin (n) x d x

\frac{1}{2} x^{2} sin (n) + C

Solution steps

\int 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 x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= sin (n) \frac{x ^{2}}{2}

Simplify

sin (n) \frac{x ^{2}}{2} : \frac{1}{2} x^{2} sin (n)

= \frac{1}{2} x^{2} sin (n)

Add a constant to the solution

= \frac{1}{2} x^{2} sin (n) + C

\int_{0}^{2} 6 - x^{2} d x

\frac{\partial}{\partial y} (2 x + 3 y)

x^{2} + 2 x + 3

\frac{d}{d x} (\frac{( - 1 ) ^{x}}{x})

18 y^{^{'}} = y^{3} - 9 y