Question

Solve ${\int }_2^{-13}\frac{dx}{\sqrt[5]{5{(3-x)}^4}}$

• A. $-5(\sqrt[5]{516}-1)$
• B. $5(\sqrt[5]{516}-1)$
• C. $-5(\sqrt[5]{516}+1)$
• D. None of these

Answer 1

Answer: (A)

$-5(\sqrt[5]{516}-1)$

Let $I={\int }_2^{-13}\frac{dx}{5\sqrt{{(3-x)}^4}}$
Put $3-x=t\Rightarrow -dx=dt$
$I={\int }_1^{16}\frac{dt}{t^{\frac{4}{5}}}={\left[\frac{t^{\frac{1}{5}}}{\frac{1}{5}}\right]}_1^{16}$
$=-5(\sqrt[5]{516}-1)$