If ∫x+5x2+4x+6 dx=alog(x2+4x+5)+btan−1(x+k)+constant then a, b, k=

∫x+5x2+4x+6dx =∫x+2+3x2+4x+5dx =∫x+2x2+4x+5+∫3(x+2)2+1dx =12log(x2+4x+5)+3tan-1(x+2)+c a=12, b=3, k=2 (a, b, k)=12, 3, 2

If ∫x+5x2+4x+6 dx=alog(x2+4x+5)+btan−1(x+k)+constant then a, b, k=

∫x+5x2+4x+6dx =∫x+2+3x2+4x+5dx =∫x+2x2+4x+5+∫3(x+2)2+1dx =12log(x2+4x+5)+3tan-1(x+2)+c a=12, b=3, k=2 (a, b, k)=12, 3, 2

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

If $\int \frac{x + 5}{x^{2} + 4 x + 6} d x = a \log (x^{2} + 4 x + 5) + b \tan^{- 1} (x + k) +$ constant then $(a, b, k) =$

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

$(\frac{1}{2}, 3, 2)$

$(\frac{1}{2}, 1, 2)$

$(\frac{1}{2}, 3, 1)$

$(1, 3, 2)$

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\int \frac{x + 5}{x^{2} + 4 x + 6} dx = \int \frac{x + 2 + 3}{x^{2} + 4 x + 5} dx = \int \frac{x + 2}{x^{2} + 4 x + 5} + \int \frac{3}{{(x + 2)}^{2} + 1} dx = \frac{1}{2} \log (x^{2} + 4 x + 5) + 3 \tan^{- 1} (x + 2) + c a = \frac{1}{2}, b = 3, k = 2 (a, b, k) = (\frac{1}{2}, 3, 2)$