What is the integral of 56\sqrt[3]{x+1} ?

The integral of 56\sqrt[3]{x+1} is 42(x+1)^{4/3}+C

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integral of 56\sqrt[3]{x+1}

42 (x + 1)^{\frac{4}{3}} + C

Solution steps

Take the constant out:

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

Apply u-substitution

Apply the Power Rule

: \frac{3}{4} u^{\frac{4}{3}}

= 56 \cdot \frac{3}{4} u^{\frac{4}{3}}

Substitute back

u = x + 1

= 56 \cdot \frac{3}{4} (x + 1)^{\frac{4}{3}}

Simplify

56 \cdot \frac{3}{4} (x + 1)^{\frac{4}{3}} : 42 (x + 1)^{\frac{4}{3}}

= 42 (x + 1)^{\frac{4}{3}}

Add a constant to the solution

= 42 (x + 1)^{\frac{4}{3}} + C

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What is the integral of 56\sqrt[3]{x+1} ?
The integral of 56\sqrt[3]{x+1} is 42(x+1)^{4/3}+C