What is the integral of (7x^3-5sqrt(x))/x ?

The integral of (7x^3-5sqrt(x))/x is (7x^3)/3-10sqrt(x)+C

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integral of (7x^3-5sqrt(x))/x

\int \frac{7 x ^{3} - 5 x}{x} d x

\frac{7 x ^{3}}{3} - 10 x + C

Solution steps

\int \frac{7 x ^{3} - 5 x}{x} d x

Expand

\frac{7 x ^{3} - 5 x}{x} : 7 x^{2} - \frac{5}{x}

= \int 7 x^{2} - \frac{5}{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 7 x^{2} d x - \int \frac{5}{x} d x

\int 7 x^{2} d x = \frac{7 x ^{3}}{3}

\int \frac{5}{x} d x = 10 x

= \frac{7 x ^{3}}{3} - 10 x

Add a constant to the solution

= \frac{7 x ^{3}}{3} - 10 x + C

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What is the integral of (7x^3-5sqrt(x))/x ?
The integral of (7x^3-5sqrt(x))/x is (7x^3)/3-10sqrt(x)+C