What is the integral of (x^3+x^2) ?

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

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integral of (x^3+x^2)

\int (x^{3} + x^{2}) d x

\frac{x ^{4}}{4} + \frac{x ^{3}}{3} + C

Solution steps

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

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

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

= \frac{x ^{4}}{4} + \frac{x ^{3}}{3}

Add a constant to the solution

= \frac{x ^{4}}{4} + \frac{x ^{3}}{3} + C

f (x) = 7 + 5 x

\frac{\partial}{\partial y} (x^{2} y - x y^{3})

\frac{d y}{d x} = - 2 x y

\int x^{3} e x^{4} + 5 d x

\int \frac{sin ( 2 x )}{sin ^{2} ( x )} d x

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