Step by step solution to "Evaluate the indefinite integral. ∫1x3dx"

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alesterp

Answered question

2021-11-06

Evaluate the indefinite integral.
$\int \frac{1}{\sqrt[3]{x}} d x$

Answer & Explanation

Obiajulu

Skilled2021-11-07Added 98 answers

Step 1
Given
$\int \frac{1}{\sqrt{3} {x}} d x$
The integral used here is
$\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + c$
Radical rule is used
$\sqrt[n]{x} = x^{\frac{1}{n}}$
Exponent rule
$\frac{1}{x^{n}} = x^{- n}$
Step 2
So the integral will be
$\int \frac{1}{\sqrt[3]{x}} d x = \int \frac{1}{{(x)}^{\frac{1}{3}}} d x$
$= \int {(x)}^{- \frac{1}{3}} d x$
$= \frac{x^{- \frac{1}{3} + 1}}{- \frac{1}{3} + 1} + c$
$= \frac{3}{2} x^{\frac{2}{3}} + c$

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