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

The integral of (sin(2x))/(x^2) is -(sin(2x))/x+2\Ci(2x)+C

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integral of (sin(2x))/(x^2)

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

- \frac{sin ( 2 x )}{x} + 2 Ci (2 x) + C

Solution steps

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

Apply Integration By Parts

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

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

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

= - \frac{sin ( 2 x )}{x} - (- 2 Ci (2 x))

Simplify

= - \frac{sin ( 2 x )}{x} + 2 Ci (2 x)

Add a constant to the solution

= - \frac{sin ( 2 x )}{x} + 2 Ci (2 x) + C

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What is the integral of (sin(2x))/(x^2) ?
The integral of (sin(2x))/(x^2) is -(sin(2x))/x+2\Ci(2x)+C