What is the integral of (2cos(x))/(x^3) ?

The integral of (2cos(x))/(x^3) is -(cos(x)}{x^2}+\frac{sin(x))/x-\Ci(x)+C

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integral of (2cos(x))/(x^3)

\int \frac{2 cos ( x )}{x ^{3}} d x

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

Solution steps

\int \frac{2 cos ( x )}{x ^{3}} d x

Take the constant out:

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

= 2 \cdot \int \frac{cos ( x )}{x ^{3}} d x

Apply Integration By Parts

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

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

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

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

Simplify

2 (- \frac{cos ( x )}{2 x ^{2}} - \frac{1}{2} (- \frac{sin ( x )}{x} + Ci (x))) : - \frac{cos ( x )}{x ^{2}} + \frac{sin ( x )}{x} - Ci (x)

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

Add a constant to the solution

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

\int sec^{4} (x) cos^{3} (x) d x

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What is the integral of (2cos(x))/(x^3) ?
The integral of (2cos(x))/(x^3) is -(cos(x)}{x^2}+\frac{sin(x))/x-\Ci(x)+C