What is the integral of 1/x+1/(x^3) ?

The integral of 1/x+1/(x^3) is ln|x|-1/(2x^2)+C

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integral of 1/x+1/(x^3)

integral

\frac{1}{x} + \frac{1}{x ^{3}}

ln ∣ x ∣ - \frac{1}{2 x ^{2}} + C

Solution steps

\int \frac{1}{x} + \frac{1}{x ^{3}} 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{1}{x} d x + \int \frac{1}{x ^{3}} d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int \frac{1}{x ^{3}} d x = - \frac{1}{2 x ^{2}}

= ln ∣ x ∣ - \frac{1}{2 x ^{2}}

Add a constant to the solution

= ln ∣ x ∣ - \frac{1}{2 x ^{2}} + C

\frac{( 3 x - 13 )}{( x ^{2} - 12 + 45 ) ^{2}}

4 x^{3} + 5 x^{4} + 3

\frac{( x + 5 )}{( - 3 x )}

sin^{3} (x) - 1

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

What is the integral of 1/x+1/(x^3) ?
The integral of 1/x+1/(x^3) is ln|x|-1/(2x^2)+C