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

The integral of (sin(x))/(2x^2) is 1/2 (-(sin(x))/x+\Ci(x))+C

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

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

\frac{1}{2} (- \frac{sin ( x )}{x} + Ci (x)) + C

Solution steps

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

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{sin ( x )}{x ^{2}} d x

Apply Integration By Parts

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

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

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

= \frac{1}{2} (- \frac{sin ( x )}{x} - (- Ci (x)))

Simplify

= \frac{1}{2} (- \frac{sin ( x )}{x} + Ci (x))

Add a constant to the solution

= \frac{1}{2} (- \frac{sin ( x )}{x} + Ci (x)) + C

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What is the integral of (sin(x))/(2x^2) ?
The integral of (sin(x))/(2x^2) is 1/2 (-(sin(x))/x+\Ci(x))+C