What is the integral of (1/(\sqrt[3]{x)}+1)^2 ?

The integral of (1/(\sqrt[3]{x)}+1)^2 is (1+\sqrt[3]{x})^3+C

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integral of (1/(\sqrt[3]{x)}+1)^2

Solution steps

Simplify

Apply exponent rule:

(a^{n})^{m} = a^{n \cdot m}

Apply u-substitution

: \int 3 u^{2} d u

= \int 3 u^{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= 3 \cdot \frac{u ^{3}}{3}

Substitute back

Simplify

Add a constant to the solution

y^{^{'}} = x y

x \to 5 lim (\frac{x π}{3})

\frac{1}{x ^{2}} d x = e^{- 2 t} d t

- x^{3} (- 1.1)

ln (1 + x^{2})

What is the integral of (1/(\sqrt[3]{x)}+1)^2 ?
The integral of (1/(\sqrt[3]{x)}+1)^2 is (1+\sqrt[3]{x})^3+C