What is the integral from 0 to 4 of (4x^3+2/(x+1)) ?

The integral from 0 to 4 of (4x^3+2/(x+1)) is 256+2ln(5)

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integral from 0 to 4 of (4x^3+2/(x+1))

\int_{0}^{4} (4 x^{3} + \frac{2}{x + 1}) d x

256 + 2 ln (5)

Decimal

259.21887 \dots

Solution steps

\int_{0}^{4} 4 x^{3} + \frac{2}{x + 1} 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_{0}^{4} 4 x^{3} d x + \int_{0}^{4} \frac{2}{x + 1} d x

\int_{0}^{4} 4 x^{3} d x = 256

\int_{0}^{4} \frac{2}{x + 1} d x = 2 ln (5)

= 256 + 2 ln (5)

\int_{- 2}^{0} \frac{1}{x ^{2} + 2 x + 2} d x

\int_{- 1}^{0} \frac{e ^{\frac{1}{x}}}{x ^{3}} d x

\int_{1}^{5} x e^{- x} d x

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

\int_{0}^{\frac{π}{4}} \frac{x}{1 + cos ( 2 x )} d x

What is the integral from 0 to 4 of (4x^3+2/(x+1)) ?
The integral from 0 to 4 of (4x^3+2/(x+1)) is 256+2ln(5)