What is the integral of (3x^4+2x)/(x^3) ?

The integral of (3x^4+2x)/(x^3) is -(3x^3+2)/x+(9x^2)/2+C

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integral of (3x^4+2x)/(x^3)

\int \frac{3 x ^{4} + 2 x}{x ^{3}} d x

- \frac{3 x ^{3} + 2}{x} + \frac{9 x ^{2}}{2} + C

Solution steps

\int \frac{3 x ^{4} + 2 x}{x ^{3}} d x

Simplify

\frac{3 x ^{4} + 2 x}{x ^{3}} : \frac{3 x ^{3} + 2}{x ^{2}}

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

Apply Integration By Parts

: - \frac{3 x ^{3} + 2}{x} - \int - 9 x d x

= - \frac{3 x ^{3} + 2}{x} - \int - 9 x d x

\int - 9 x d x = - \frac{9 x ^{2}}{2}

= - \frac{3 x ^{3} + 2}{x} - (- \frac{9 x ^{2}}{2})

Simplify

= - \frac{3 x ^{3} + 2}{x} + \frac{9 x ^{2}}{2}

Add a constant to the solution

= - \frac{3 x ^{3} + 2}{x} + \frac{9 x ^{2}}{2} + C

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What is the integral of (3x^4+2x)/(x^3) ?
The integral of (3x^4+2x)/(x^3) is -(3x^3+2)/x+(9x^2)/2+C