The integral $\int \frac{d x}{x^{2} {(x^{4} + 1)}^{\frac{3}{4}}} =$

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

$- {(\frac{x^{4} + 1}{x^{4}})}^{\frac{1}{4}} + c$

${(\frac{x^{4} + 1}{x^{4}})}^{\frac{1}{4}} + c$

${(x^{4} + 1)}^{\frac{1}{4}} + c$

$- {(x^{4} + 1)}^{\frac{1}{4}} + c$

answer is A.

(Unlock A.I Detailed Solution for FREE)

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$I = \int \frac{d x}{x^{5} {(1 + \frac{1}{x^{4}})}^{3 / 4}}$ put $1 + \frac{1}{x^{4}} = t$ then $- \frac{4}{x^{5}} d x = d t$

$I = - \frac{1}{4} \int \frac{d t}{t^{3 / 4}}$

$= - \frac{1}{4} \frac{t^{\frac{- 3}{4} + 1}}{- \frac{3}{4} + 1} + c$ = $- \frac{1}{4} \times 4 {(1 + \frac{1}{x^{4}})}^{1 / 4} + c$

Watch 3-min video & get full concept clarity

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test