Find the integral of 5 x 4 x 5 + 9 :

Question

Find the integral of $\frac{5 x^{4}}{\sqrt{x^{5} + 9}}$ :

Smart Achievers · Accepted Answer

(4)

Ans. $2 \sqrt{x^{5} + 9} + C$

Explanation:

Let $x^{5} + 9 = t$

Differentiating with respect to $x$ , we get

$5 x^{4} d x = d t$

$\int \frac{5 x^{4}}{\sqrt{x^{5} + 9}} d x = \int \frac{d t}{\sqrt{t}}$

$= \frac{t^{- \frac{1}{2} + 1}}{- \frac{1}{2} + 1} + C$

$= 2 \sqrt{t} + C$

Replacing $t$ with $x^{5} + 9$ , we get

$\int \frac{5 x^{4}}{\sqrt{x^{5} + 9}} d x = 2 \sqrt{x^{5} + 9} + C$

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