∫x.logx(x2−1)3 dx=

∫x logxx2-13dx =∫ logxx(x2-1)32dx =(log x) -1x2-1-∫1x-1x2-1dx =-log xx2-1+sec-1x+cNote : ∫x(x2-1)32dx =12∫dtt32 =12t-12-12 =-1t=-1x2-1

∫x.logx(x2−1)3 dx=

∫x logxx2-13dx =∫ logxx(x2-1)32dx =(log x) -1x2-1-∫1x-1x2-1dx =-log xx2-1+sec-1x+cNote : ∫x(x2-1)32dx =12∫dtt32 =12t-12-12 =-1t=-1x2-1

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

$\int \frac{x . \log x}{{(\sqrt{x^{2} - 1})}^{3}} d x =$

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$S e c^{- 1} x + \frac{\log x}{\sqrt{x^{2} - 1}} + c$

$S e c^{- 1} x - \frac{\log x}{\sqrt{x^{2} - 1}} + c$

$\frac{\log x}{\sqrt{x^{2} - 1}} - S e c^{- 1} x + c$

$\frac{- \log x}{\sqrt{x^{2} - 1}} - S e c^{- 1} x + c$

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\int \frac{x logx}{{(\sqrt{x^{2} - 1})}^{3}} dx = \int logx \frac{x}{{(x^{2} - 1)}^{\frac{3}{2}}} dx = (\log x) (- \frac{1}{\sqrt{x^{2} - 1}}) - \int \frac{1}{x} (- \frac{1}{\sqrt{x^{2} - 1}}) dx = - \frac{\log x}{\sqrt{x^{2} - 1}} + \sec^{- 1} x + c$ $Note : \int \frac{x}{{(x^{2} - 1)}^{\frac{3}{2}}} dx = \frac{1}{2} \int \frac{dt}{t^{\frac{3}{2}}} = \frac{1}{2} (\frac{t^{\frac{- 1}{2}}}{\frac{- 1}{2}}) = \frac{- 1}{\sqrt{t}} = \frac{- 1}{\sqrt{x^{2} - 1}}$