What is the integral of (1-2x^5)/x ?

The integral of (1-2x^5)/x is ln|x|-(2x^5)/5+C

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integral of (1-2x^5)/x

\int \frac{1 - 2 x ^{5}}{x} d x

ln ∣ x ∣ - \frac{2 x ^{5}}{5} + C

Solution steps

\int \frac{1 - 2 x ^{5}}{x} d x

Expand

\frac{1 - 2 x ^{5}}{x} : \frac{1}{x} - 2 x^{4}

= \int \frac{1}{x} - 2 x^{4} 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 2 x^{4} d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int 2 x^{4} d x = \frac{2 x ^{5}}{5}

= ln ∣ x ∣ - \frac{2 x ^{5}}{5}

Add a constant to the solution

= ln ∣ x ∣ - \frac{2 x ^{5}}{5} + C

\int_{0}^{1} (1 - x^{2})^{\frac{3}{2}} d x

\int \frac{15}{x ^{2} + 1} d x

e^{17 x}

f (x) = x ln (x)

What is the integral of (1-2x^5)/x ?
The integral of (1-2x^5)/x is ln|x|-(2x^5)/5+C