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

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

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

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

- \frac{( x ^{2} + 3 ) ^{2}}{x} + 4 (\frac{x ^{3}}{3} + 3 x) + C

Solution steps

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

Apply Integration By Parts

: - \frac{( x ^{2} + 3 ) ^{2}}{x} - \int - 4 (x^{2} + 3) d x

= - \frac{( x ^{2} + 3 ) ^{2}}{x} - \int - 4 (x^{2} + 3) d x

\int - 4 (x^{2} + 3) d x = - 4 (\frac{x ^{3}}{3} + 3 x)

= - \frac{( x ^{2} + 3 ) ^{2}}{x} - (- 4 (\frac{x ^{3}}{3} + 3 x))

Simplify

= - \frac{( x ^{2} + 3 ) ^{2}}{x} + 4 (\frac{x ^{3}}{3} + 3 x)

Add a constant to the solution

= - \frac{( x ^{2} + 3 ) ^{2}}{x} + 4 (\frac{x ^{3}}{3} + 3 x) + C

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