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

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

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

integral

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

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

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

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

Simplify

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

Add a constant to the solution

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

\frac{2 x + 4}{x ^{3} - 1}

3 x (1 + x)^{- 4}

\frac{u ^{2}}{( u ^{2} + 1 )}

cos^{4} (x) sin^{5} (x)

3^{x + 2}

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