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

The integral from 1 to 3 of (1+2x-4x^3) is -70

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

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

- 70

Solution steps

\int_{1}^{3} 1 + 2 x - 4 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_{1}^{3} 1 d x + \int_{1}^{3} 2 x d x - \int_{1}^{3} 4 x^{3} d x

\int_{1}^{3} 1 d x = 2

\int_{1}^{3} 2 x d x = 8

\int_{1}^{3} 4 x^{3} d x = 80

= 2 + 8 - 80

Simplify

= - 70

\frac{1}{( s ^{2} + 3 s + 2 ) ( s + 1 )}

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

\int \frac{x ^{2} + 4 x - 7}{x - 1} d x

\frac{d}{d x} (\frac{8 x - 1}{6 x + 7})

\int - ln (x) - \frac{ln ( x )}{4} d x

What is the integral from 1 to 3 of (1+2x-4x^3) ?
The integral from 1 to 3 of (1+2x-4x^3) is -70