CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Find 13+2sinx+cosxdx.

Open in App
Solution

Let dx3+2sinx+cosx
Put tan(x2)=t
x=2tan1t
dx=2dt1+t2 and sinx=2t1+t2,cosx=1t21+t2
I=13+2(2t1+t2)+(1t21+t2).2dt1+t2
=1+t23(1+t2)+4t+(1t2).2dt1+t2
=2dt2t2+4t+4
=dtt2+2t+2
=dt(t2+2t+1)+1
=dt(t+1)2+12
=11tan1(t+11)+c
=tan1[tan(x2)+1]+c

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Integration by Partial Fractions
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon