What is the integral of (x^4-2x^2+1)/(x^2) ?

The integral of (x^4-2x^2+1)/(x^2) is (x^3)/3-2x-1/x+C

Popular >

integral of (x^4-2x^2+1)/(x^2)

\int \frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}} d x

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

Solution steps

\int \frac{x ^{4} - 2 x ^{2} + 1}{x ^{2}} d x

Expand

\frac{x ^{4} - 2 x ^{2} + 1}{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 \frac{1}{e ^{x} + 7} d x

\int 20 (50 + x) d x

\int \frac{cos ( x )}{sin ( x ) ln ( sin ( x ) )} d x

\int - sin (2 x) tan (2 x) d x

\int x \cdot arctan (2 x) d x

What is the integral of (x^4-2x^2+1)/(x^2) ?
The integral of (x^4-2x^2+1)/(x^2) is (x^3)/3-2x-1/x+C