What is the integral of (sqrt(x)+6x^3)/x ?

The integral of (sqrt(x)+6x^3)/x is 2sqrt(x)+2x^3+C

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integral of (sqrt(x)+6x^3)/x

\int \frac{x + 6 x ^{3}}{x} d x

2 x + 2 x^{3} + C

Solution steps

\int \frac{x + 6 x ^{3}}{x} d x

Expand

\frac{x + 6 x ^{3}}{x} : \frac{1}{x} + 6 x^{2}

= \int \frac{1}{x} + 6 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{1}{x} d x + \int 6 x^{2} d x

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

\int 6 x^{2} d x = 2 x^{3}

= 2 x + 2 x^{3}

Add a constant to the solution

= 2 x + 2 x^{3} + C

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What is the integral of (sqrt(x)+6x^3)/x ?
The integral of (sqrt(x)+6x^3)/x is 2sqrt(x)+2x^3+C