What is the integral of ((3x^3+2x)/x) ?

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

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integral of ((3x^3+2x)/x)

\int (\frac{3 x ^{3} + 2 x}{x}) d x

x^{3} + 2 x + C

Solution steps

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

Expand

\frac{3 x ^{3} + 2 x}{x} : \frac{3 x ^{3}}{x} + \frac{2 x}{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{3 x ^{3}}{x} d x + \int \frac{2 x}{x} d x

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

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

= x^{3} + 2 x

Add a constant to the solution

= x^{3} + 2 x + C

y = x + 2, y = x^{2}

\frac{d}{d x} (\frac{25 - x ^{2} - y ^{2}}{y})

x \to \frac{π}{2} lim (tan (\frac{x}{2}))

\frac{d}{d x} (f (x) (1 x^{2} - 1))

tan (x)

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