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

The integral of x^4-2x^2+1 is (x^5)/5-(2x^3)/3+x+C

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integral of x^4-2x^2+1

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

\frac{x ^{5}}{5} - \frac{2 x ^{3}}{3} + x + C

Solution steps

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

\int x^{4} d x = \frac{x ^{5}}{5}

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

\int 1 d x = x

= \frac{x ^{5}}{5} - \frac{2 x ^{3}}{3} + x

Add a constant to the solution

= \frac{x ^{5}}{5} - \frac{2 x ^{3}}{3} + x + C

\int (8 x - 9) d x

\int \frac{2 - 3 x ^{2}}{5 x ^{3} - 10 x + 5} d x

\frac{\partial}{\partial x} (x^{2} y e^{\frac{y}{z}})

\frac{\partial}{\partial x} (x + y)

x \to \infty lim (4 x^{3} (e^{- \frac{2}{x ^{3}}} - 1))

What is the integral of x^4-2x^2+1 ?
The integral of x^4-2x^2+1 is (x^5)/5-(2x^3)/3+x+C