What is the integral of ((x^3+1)^2)/(x^2) ?

The integral of ((x^3+1)^2)/(x^2) is -((x^3+1)^2)/x+6((x^5)/5+(x^2)/2)+C

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integral of ((x^3+1)^2)/(x^2)

\int \frac{( x ^{3} + 1 ) ^{2}}{x ^{2}} d x

- \frac{( x ^{3} + 1 ) ^{2}}{x} + 6 (\frac{x ^{5}}{5} + \frac{x ^{2}}{2}) + C

Solution steps

\int \frac{( x ^{3} + 1 ) ^{2}}{x ^{2}} d x

Apply Integration By Parts

: - \frac{( x ^{3} + 1 ) ^{2}}{x} - \int - 6 x (x^{3} + 1) d x

= - \frac{( x ^{3} + 1 ) ^{2}}{x} - \int - 6 x (x^{3} + 1) d x

\int - 6 x (x^{3} + 1) d x = - 6 (\frac{x ^{5}}{5} + \frac{x ^{2}}{2})

= - \frac{( x ^{3} + 1 ) ^{2}}{x} - (- 6 (\frac{x ^{5}}{5} + \frac{x ^{2}}{2}))

Simplify

= - \frac{( x ^{3} + 1 ) ^{2}}{x} + 6 (\frac{x ^{5}}{5} + \frac{x ^{2}}{2})

Add a constant to the solution

= - \frac{( x ^{3} + 1 ) ^{2}}{x} + 6 (\frac{x ^{5}}{5} + \frac{x ^{2}}{2}) + C

\frac{d}{d x} y = sec (2 x)

f (x) = 2 x x - 2, at x = 3

∣ 10 x ∣, x^{2} - 11

x \to 4 lim ((x^{2} - 8) (4 x - 8))

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

What is the integral of ((x^3+1)^2)/(x^2) ?
The integral of ((x^3+1)^2)/(x^2) is -((x^3+1)^2)/x+6((x^5)/5+(x^2)/2)+C