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

Assertion :x4+1x6+1dx=tan1x+13tan1x3+C Reason: cosx+xsinxx(x+cosx)dx=log(x2+xcosx)+C

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
Assertion is correct but Reason is incorrect
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
Both Assertion and Reason are incorrect
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C Assertion is correct but Reason is incorrect
Assertion(A): x4+1x6+1dx
=(x4+1x2)+x2(x4x2+1)(x2+1)dx
=dx1+x2+x2dx1+(x3)2
Put x3=t in the second integral
x2dx=dt3
=tan1x+13dt1+t2
=tan1x+13tan1x3+C
Assertion (A) is correct.
Reason(R): cosx+xsinxx(x+cosx)dx
=(cosx+x)x(1sinx)x(x+cosx)dx
=1xdx1sinx(x+cosx)dx
Put x+cosx=t
(1sinx)dx=dt
=logxdtt
=logxlog(x+cosx)+C
=log(xx+cosx)+C
Reason (R) is false.

flag
Suggest Corrections
thumbs-up
0
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Animal Tissues
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon