What is the integral of sin(2a)x ?

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

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integral of sin(2a)x

\int sin (2 a) x d x

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

Solution steps

\int sin (2 a) x d x

Take the constant out:

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

= sin (2 a) \cdot \int x d x

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{x + 5}{x ^{2} + x - 6})

f (x) = x^{\frac{1}{5}} + 8

(- 2, 0), (0, - 4)

x \to 3 lim (h (x) - g (x))

\int π^{2 x} d x