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

The integral of (5x-1)(3x^2+2) is (15x^4)/4+5x^2-x^3-2x+C

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integral of (5x-1)(3x^2+2)

\int (5 x - 1) (3 x^{2} + 2) d x

\frac{15 x ^{4}}{4} + 5 x^{2} - x^{3} - 2 x + C

Solution steps

\int (5 x - 1) (3 x^{2} + 2) d x

Expand

(5 x - 1) (3 x^{2} + 2) : 15 x^{3} + 10 x - 3 x^{2} - 2

= \int 15 x^{3} + 10 x - 3 x^{2} - 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 15 x^{3} d x + \int 10 x d x - \int 3 x^{2} d x - \int 2 d x

\int 15 x^{3} d x = \frac{15 x ^{4}}{4}

\int 10 x d x = 5 x^{2}

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

\int 2 d x = 2 x

= \frac{15 x ^{4}}{4} + 5 x^{2} - x^{3} - 2 x

Add a constant to the solution

= \frac{15 x ^{4}}{4} + 5 x^{2} - x^{3} - 2 x + C

\int e^{x^{3}} (12 x^{2}) d x

\frac{\partial}{\partial x} (x e^{- \frac{y}{x}})

f (t) = \frac{3}{5} e^{- t} - \frac{22}{5} e^{4 t}

\int (\frac{3}{x ^{2}} - 1) d x

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

What is the integral of (5x-1)(3x^2+2) ?
The integral of (5x-1)(3x^2+2) is (15x^4)/4+5x^2-x^3-2x+C