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

The integral of sin(2x)2x is d^2(-1/2 xcos(2x)+1/4 sin(2x))+C

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integral of sin(2x)2x

\int sin (2 x) d^{2} x d x

d^{2} (- \frac{1}{2} x cos (2 x) + \frac{1}{4} sin (2 x)) + C

Solution steps

\int sin (2 x) d^{2} x d x

Take the constant out:

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

= d^{2} \cdot \int sin (2 x) x d x

Apply Integration By Parts

: - \frac{1}{2} x cos (2 x) - \int - \frac{1}{2} cos (2 x) d x

= d^{2} (- \frac{1}{2} x cos (2 x) - \int - \frac{1}{2} cos (2 x) d x)

\int - \frac{1}{2} cos (2 x) d x = - \frac{1}{4} sin (2 x)

= d^{2} (- \frac{1}{2} x cos (2 x) - (- \frac{1}{4} sin (2 x)))

Simplify

= d^{2} (- \frac{1}{2} x cos (2 x) + \frac{1}{4} sin (2 x))

Add a constant to the solution

= d^{2} (- \frac{1}{2} x cos (2 x) + \frac{1}{4} sin (2 x)) + C

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

\int \frac{x + 5}{x - 3} d x

\int - 300 v + 360 d v

\int (3 x - 7)^{5} d x

\frac{6}{x ^{2}}

What is the integral of sin(2x)2x ?
The integral of sin(2x)2x is d^2(-1/2 xcos(2x)+1/4 sin(2x))+C