What is the integral of sin(a)x ?

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

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integral of sin(a)x

\int sin (a) x d x

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

Solution steps

\int sin (a) x d x

Take the constant out:

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

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

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

\frac{1}{s ^{2} + 3 s + 2}

\frac{d}{d x} (4 sec (5 x))

f (t) = \frac{t ^{2}}{t ^{3} + 1}

\frac{d}{d x} (2 arctanh (x))

\frac{y ^{\frac{3}{2}}}{3} - y^{\frac{1}{2}}