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

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

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

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

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

Solution steps

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

\int 3 d x = 3 x

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

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

Add a constant to the solution

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

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