What is the integral of (4x^5+10x^3)/(x^2) ?

The integral of (4x^5+10x^3)/(x^2) is x^4+5x^2+C

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integral of (4x^5+10x^3)/(x^2)

\int \frac{4 x ^{5} + 10 x ^{3}}{x ^{2}} d x

x^{4} + 5 x^{2} + C

Solution steps

\int \frac{4 x ^{5} + 10 x ^{3}}{x ^{2}} d x

Expand

\frac{4 x ^{5} + 10 x ^{3}}{x ^{2}} : \frac{4 x ^{5}}{x ^{2}} + \frac{10 x ^{3}}{x ^{2}}

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{4 x ^{5}}{x ^{2}} d x + \int \frac{10 x ^{3}}{x ^{2}} d x

\int \frac{4 x ^{5}}{x ^{2}} d x = x^{4}

\int \frac{10 x ^{3}}{x ^{2}} d x = 5 x^{2}

= x^{4} + 5 x^{2}

Add a constant to the solution

= x^{4} + 5 x^{2} + C

\int \frac{3 x - 5}{x} d x

\frac{d y}{d x} = 0.72 - \frac{9 y}{1000}, y (0) = 80

\int_{- 1}^{1} x (x^{2} + 9)^{3} d x

y \frac{d y}{d x} + 8 x^{3} = 4

What is the integral of (4x^5+10x^3)/(x^2) ?
The integral of (4x^5+10x^3)/(x^2) is x^4+5x^2+C