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

The integral of (2x+1)(x-3) is (2x^3)/3-(5x^2)/2-3x+C

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integral of (2x+1)(x-3)

\int (2 x + 1) (x - 3) d x

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

Solution steps

\int (2 x + 1) (x - 3) d x

Expand

(2 x + 1) (x - 3) : 2 x^{2} - 5 x - 3

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

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (tan (x y^{3}))

9 y^{^{''}} + 6 y^{^{'}} + y = 0, y (0) = 1, y^{^{'}} (0) = 2

(7 x^{2} - 11 x) e^{x}

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

\frac{d}{d x} (x^{5} - e^{x} ln (x))

What is the integral of (2x+1)(x-3) ?
The integral of (2x+1)(x-3) is (2x^3)/3-(5x^2)/2-3x+C