wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

x2-1(x4+3x2+1)tan-1x+1xdx=


A

tan-1x+1x+c

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

cot-1x+1x+c

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

logx+1x+c

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

logtan-1x+1x+c

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D

logtan-1x+1x+c


Explanation for the correct answer.

Evaluate the given integral.

An integral I=x2-1(x4+3x2+1)tan-1x+1xdx is given.

Rewrite the given integral as follows:

I=1-1x2x2+3+1x2tan-1x+1xdxI=1-1x2x+1x2+1tan-1x+1xdx

Now, assume that, x+1x=u

Differentiate both sides with respect to x.

1-1x2dx=du

Write the integral in terms of u by substituting x+1x=u.

I=1u2+1tan-1udu

Again, Assume that tan-1u=v.

Differentiate both sides with respect to u.

1u2+1du=dv

Write the integral in terms of v by substituting tan-1u=v.

I=1vdvI=log(v)+c

Substitute back tan-1u=v.

I=log(tan-1u)+c

Substitute back x+1x=u.

I=logtan-1x+1x+c

Therefore, after evaluating the given integral we get logtan-1x+1x+c.

Hence, option D is the correct answer.


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