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

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

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

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

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

Solution steps

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

Expand

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

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

\int sin^{4} (\frac{x}{2}) d x

x \to 4 lim (x^{2} + 2 x - 13)

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

\frac{\partial}{\partial x} (\frac{( x + y )}{z})

\int - 4 e^{- x} d x

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