How do you integrate $\int \frac{x^{3} + x}{x} d x$ $int (x^3+x)/x dx$ ?

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How do you integrate $\int \frac{x^{3} + x}{x} d x$ $int (x^3+x)/x dx$ ?

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Answer 1 · 2016-10-07T13:26:48

$\frac{x^{3}}{3} + x + C$ $x^3/3+x+C$

Explanation:

First start off by simplifying:

$\int \frac{x^{3} + x}{x} d x$ $int(x^3+x)/xdx$ =
$\int \frac{x^{3}}{x} + \frac{x}{x} d x$ $intx^3/x+x/xdx$ =
$\int x^{2} + 1 d x$ $intx^2+1dx$ =
$\int x^{2} d x + \int 1 d x$ $intx^2dx+int1dx$ =
$\frac{x^{3}}{3} + x + C$ $x^3/3+x+C$

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How do you integrate $\int \frac{x^{3} + x}{x} d x$ $int (x^3+x)/x dx$ ?

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