RD Sharma Class 12 Solutions - Indefinite Integrals - 3

# RD Sharma Class 12 Solutions - Indefinite Integrals - 3 | Mathematics (Maths) Class 12 - JEE PDF Download

``` Page 1

27. Question
Evaluate the following integrals:
Let
Let
Also,
cos t =x
Thus,
Now let us solve this by ‘by parts’ method
Using integration by parts,
Let
U=t; du=dt
Thus,
Substituting
28. Question
Evaluate the following integrals:
We know that integration by parts is given by:
Page 2

27. Question
Evaluate the following integrals:
Let
Let
Also,
cos t =x
Thus,
Now let us solve this by ‘by parts’ method
Using integration by parts,
Let
U=t; du=dt
Thus,
Substituting
28. Question
Evaluate the following integrals:
We know that integration by parts is given by:
Choosing log x as first function and  as second function we get,
+c
+ c
29. Question
Evaluate the following integrals:
? cosec
3
x dx
Let
Using integration by parts,
We know that,
Using integration by parts,
30. Question
Page 3

27. Question
Evaluate the following integrals:
Let
Let
Also,
cos t =x
Thus,
Now let us solve this by ‘by parts’ method
Using integration by parts,
Let
U=t; du=dt
Thus,
Substituting
28. Question
Evaluate the following integrals:
We know that integration by parts is given by:
Choosing log x as first function and  as second function we get,
+c
+ c
29. Question
Evaluate the following integrals:
? cosec
3
x dx
Let
Using integration by parts,
We know that,
Using integration by parts,
30. Question
Evaluate the following integrals:
? sec
–1
vx dx
Let
dx=2tdt
Using integration by parts,
We know that,
Substitute value for t,
31. Question
Evaluate the following integrals:
? sin
–1
vx dx
Let
dx=2tdt
Using integration by parts,
We know that,
Page 4

27. Question
Evaluate the following integrals:
Let
Let
Also,
cos t =x
Thus,
Now let us solve this by ‘by parts’ method
Using integration by parts,
Let
U=t; du=dt
Thus,
Substituting
28. Question
Evaluate the following integrals:
We know that integration by parts is given by:
Choosing log x as first function and  as second function we get,
+c
+ c
29. Question
Evaluate the following integrals:
? cosec
3
x dx
Let
Using integration by parts,
We know that,
Using integration by parts,
30. Question
Evaluate the following integrals:
? sec
–1
vx dx
Let
dx=2tdt
Using integration by parts,
We know that,
Substitute value for t,
31. Question
Evaluate the following integrals:
? sin
–1
vx dx
Let
dx=2tdt
Using integration by parts,
We know that,
t=sin u;dt=cos u du
There fore,
32. Question
Evaluate the following integrals:
? x tan
2
x dx
Let
Using integration by parts,
We know that,
33. Question
Page 5

27. Question
Evaluate the following integrals:
Let
Let
Also,
cos t =x
Thus,
Now let us solve this by ‘by parts’ method
Using integration by parts,
Let
U=t; du=dt
Thus,
Substituting
28. Question
Evaluate the following integrals:
We know that integration by parts is given by:
Choosing log x as first function and  as second function we get,
+c
+ c
29. Question
Evaluate the following integrals:
? cosec
3
x dx
Let
Using integration by parts,
We know that,
Using integration by parts,
30. Question
Evaluate the following integrals:
? sec
–1
vx dx
Let
dx=2tdt
Using integration by parts,
We know that,
Substitute value for t,
31. Question
Evaluate the following integrals:
? sin
–1
vx dx
Let
dx=2tdt
Using integration by parts,
We know that,
t=sin u;dt=cos u du
There fore,
32. Question
Evaluate the following integrals:
? x tan
2
x dx
Let
Using integration by parts,
We know that,
33. Question
Evaluate the following integrals:
Let  it can be written n terms of cos x
Using integration by parts,
34. Question
Evaluate the following integrals:
? (x + 1)e
x
log(xe
x
) dx
Let
Using integration by parts,
```

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

### Up next

 Explore Courses for JEE exam
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

;