What is the integral of x^3+2x^2-x+k ?

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

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integral of x^3+2x^2-x+k

\int x^{3} + 2 x^{2} - x + k d x

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

Solution steps

\int x^{3} + 2 x^{2} - x + k 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^{3} d x + \int 2 x^{2} d x - \int x d x + \int k d x

\int x^{3} d x = \frac{x ^{4}}{4}

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

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

\int k d x = k x

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

Add a constant to the solution

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

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

\int \frac{1 + x}{1 - x} d x

\frac{\partial}{\partial y} (ln (2 x + y + 1))

\int - 4 e^{- \frac{x}{4}} d x

(x, y) \to (2, 1) lim (\frac{x - 2 y}{x ^{3} - 8 y ^{3}})

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