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

The integral of (x^4+3sqrt(x))/(x^2) is (x^3)/3-6/(sqrt(x))+C

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

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

\frac{x ^{3}}{3} - \frac{6}{x} + C

Solution steps

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

Expand

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

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

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

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

= \frac{x ^{3}}{3} - \frac{6}{x}

Add a constant to the solution

= \frac{x ^{3}}{3} - \frac{6}{x} + C

\frac{e ^{x^{2}}}{e ^{x}}

f (x) = e^{x} sin^{2} (x)

\int_{0}^{t} t e^{- t} d t

\frac{\partial}{\partial x} (e^{x - 2})

\frac{d}{d x} (8 x^{3} + 4 x^{2} - 5 x + 4)

What is the integral of (x^4+3sqrt(x))/(x^2) ?
The integral of (x^4+3sqrt(x))/(x^2) is (x^3)/3-6/(sqrt(x))+C