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Popular >

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

Solution

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

Solution

\frac{2 x ^{5}}{5} - 2 x + C

Solution steps

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

Expand

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

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

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

\int \frac{1}{x} d x = 2 x

= \frac{2 x ^{5}}{5} - 2 x

Add a constant to the solution

= \frac{2 x ^{5}}{5} - 2 x + C

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Frequently Asked Questions (FAQ)

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