What is the integral of 5x^2+3x+2 ?

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

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integral of 5x^2+3x+2

\int 5 x^{2} + 3 x + 2 d x

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

Solution steps

\int 5 x^{2} + 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 5 x^{2} d x + \int 3 x d x + \int 2 d x

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

\int_{0}^{5} (1 + 2 x^{3}) d x

\frac{\partial}{\partial x} (x arctan (x + 2 y))

\frac{d}{d x} (\frac{2 cos ( x )}{x + 1})

\int \frac{( x - 2 )}{2} d x

\frac{d}{d x} (\frac{10 x}{x ^{2} - 6})

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