What is the integral of 2x^2+3x-1 ?

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

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integral of 2x^2+3x-1

\int 2 x^{2} + 3 x - 1 d x

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

Solution steps

\int 2 x^{2} + 3 x - 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 2 x^{2} d x + \int 3 x d x - \int 1 d x

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

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

\int 1 d x = x

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

Add a constant to the solution

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

f (x) = \frac{x}{x ^{2} + 5}

\int_{0}^{3} x^{2} e^{- x} d x

x^{\frac{5}{2}}

\int (lo g_{e} (x))^{2} d x

\int \frac{x ^{2} + 4}{x} d x

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