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

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

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

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

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

Solution steps

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

Expand

(5 x - 1) (3 x^{3} + 2) : 15 x^{4} + 10 x - 3 x^{3} - 2

= \int 15 x^{4} + 10 x - 3 x^{3} - 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^{4} d x + \int 10 x d x - \int 3 x^{3} d x - \int 2 d x

\int 15 x^{4} d x = 3 x^{5}

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

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

x \to \infty lim (x (arctan (x) - \frac{π}{2}))

f (x) = (7 x^{6} + 8 x^{3})^{4}

4 y^{^{''}} - 4 y^{^{'}} - 3 y = 0, y (0) = 1, y^{^{'}} (0) = 5

x \to 0 + lim ((cot (x))^{s i n (x)})

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