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

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

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

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

\frac{x ^{2}}{2} + 2 x + C

Solution steps

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

Simplify

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

= \int 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 x d x + \int 2 d x

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

\int 2 d x = 2 x

= \frac{x ^{2}}{2} + 2 x

Add a constant to the solution

= \frac{x ^{2}}{2} + 2 x + C

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