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

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

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

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

\frac{x ^{3}}{3} + 2 x - \frac{1}{x} + C

Solution steps

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

Expand

\frac{( x ^{2} + 1 ) ^{2}}{x ^{2}} : x^{2} + 2 + \frac{1}{x ^{2}}

= \int x^{2} + 2 + \frac{1}{x ^{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 2 d x + \int \frac{1}{x ^{2}} d x

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

\int 2 d x = 2 x

\int \frac{1}{x ^{2}} d x = - \frac{1}{x}

= \frac{x ^{3}}{3} + 2 x - \frac{1}{x}

Add a constant to the solution

= \frac{x ^{3}}{3} + 2 x - \frac{1}{x} + C

\int cos (x) (e^{7 s i n (x)}) d x

\frac{( - 8 x )}{2 x - 1}

y^{^{'}} = \frac{2 x y ^{2} + 8 x}{( x ^{2} y + 3 y )}

x \to 0 + lim ((e^{x} - 1)^{x})

\int t (ln (t))^{2} d t

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