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 Notation

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_{- 4}^{- 3} - x^{2} - 3 x d x

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

\int_{1}^{2} x^{2} ln (x^{3}) d x

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

\int_{0}^{1} 9 x^{2} 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)