What is the integral of (u^4-u^3+u^2) ?

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

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integral of (u^4-u^3+u^2)

\int (u^{4} - u^{3} + u^{2}) d u

\frac{u ^{5}}{5} - \frac{u ^{4}}{4} + \frac{u ^{3}}{3} + C

Solution steps

\int u^{4} - u^{3} + u^{2} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u^{4} d u - \int u^{3} d u + \int u^{2} d u

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

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

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

= \frac{u ^{5}}{5} - \frac{u ^{4}}{4} + \frac{u ^{3}}{3}

Add a constant to the solution

= \frac{u ^{5}}{5} - \frac{u ^{4}}{4} + \frac{u ^{3}}{3} + C

\frac{\partial}{\partial x} (4 y - 2 x y)

sin (2 x)

x \to 2 lim (\frac{1}{( x - 2 )})

\int \frac{2 x ^{3} + x ^{2} - 7 x + 7}{x ^{2} + x - 2} d x

\frac{\partial}{\partial y} (x y e^{4 y})

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