What is the integral of (5x^7-9x^5)/(x^3) ?

The integral of (5x^7-9x^5)/(x^3) is 1/3 x^3(5x^2-9)-(2x^5)/3+C

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integral of (5x^7-9x^5)/(x^3)

\int \frac{5 x ^{7} - 9 x ^{5}}{x ^{3}} d x

\frac{1}{3} x^{3} (5 x^{2} - 9) - \frac{2 x ^{5}}{3} + C

Solution steps

\int \frac{5 x ^{7} - 9 x ^{5}}{x ^{3}} d x

Simplify

\frac{5 x ^{7} - 9 x ^{5}}{x ^{3}} : x^{2} (5 x^{2} - 9)

= \int x^{2} (5 x^{2} - 9) d x

Apply Integration By Parts

: \frac{1}{3} x^{3} (5 x^{2} - 9) - \int \frac{10 x ^{4}}{3} d x

= \frac{1}{3} x^{3} (5 x^{2} - 9) - \int \frac{10 x ^{4}}{3} d x

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

= \frac{1}{3} x^{3} (5 x^{2} - 9) - \frac{2 x ^{5}}{3}

Add a constant to the solution

= \frac{1}{3} x^{3} (5 x^{2} - 9) - \frac{2 x ^{5}}{3} + C

f (x) = \frac{2 x}{2 + x}

\frac{\partial}{\partial x} (4 x cos (y))

5 sin (4 t)

\frac{\partial}{\partial z} (x^{y})

(x^{2} + 1) \frac{d y}{d x} + 3 x (y - 1) = 0

What is the integral of (5x^7-9x^5)/(x^3) ?
The integral of (5x^7-9x^5)/(x^3) is 1/3 x^3(5x^2-9)-(2x^5)/3+C