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

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

Popular >

integral of (2x-3)(4x^2+1)

\int (2 x - 3) (4 x^{2} + 1) d x

2 x^{4} + x^{2} - 4 x^{3} - 3 x + C

Solution steps

\int (2 x - 3) (4 x^{2} + 1) d x

Expand

(2 x - 3) (4 x^{2} + 1) : 8 x^{3} + 2 x - 12 x^{2} - 3

= \int 8 x^{3} + 2 x - 12 x^{2} - 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 8 x^{3} d x + \int 2 x d x - \int 12 x^{2} d x - \int 3 d x

\int 8 x^{3} d x = 2 x^{4}

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

\int 12 x^{2} d x = 4 x^{3}

\int 3 d x = 3 x

= 2 x^{4} + x^{2} - 4 x^{3} - 3 x

Add a constant to the solution

= 2 x^{4} + x^{2} - 4 x^{3} - 3 x + C

\frac{d}{d x} (\frac{5 x}{x - 2})

x \to - 2 lim (\frac{7}{x ^{2}})

x \to 7 - lim (\frac{( x + 8 )}{x - 7})

\int sin (2 x) \cdot cos (x) d x

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

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