What is area y=(x^3+1)^{-1},x=0,x=1 ?

The answer to area y=(x^3+1)^{-1},x=0,x=1 is 1/3 ln(2)+pi/(3sqrt(3))

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area y=(x^3+1)^{-1},x=0,x=1

area

y = (x^{3} + 1)^{- 1}, x = 0, x = 1

\frac{1}{3} ln (2) + \frac{π}{3 3}

Solution steps

Apply the area formula:

\int_{0}^{1} \frac{1}{∣ x ^{3} + 1 ∣} d x

Solve

\int_{0}^{1} \frac{1}{∣ x ^{3} + 1 ∣} d x : \frac{1}{3} ln (2) + \frac{π}{3 3}

The area is:

= \frac{1}{3} ln (2) + \frac{π}{3 3}

\int x^{2} + 4 x + 4 d x

\int_{0}^{4} - x + 1 d x

x \to \infty lim (\frac{x}{6 + e ^{x}})

\int (\frac{4 - t + t ^{2}}{t ^{2}}) d t

\frac{d}{d x} (ln (x^{2} + 20))

What is area y=(x^3+1)^{-1},x=0,x=1 ?
The answer to area y=(x^3+1)^{-1},x=0,x=1 is 1/3 ln(2)+pi/(3sqrt(3))