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

 Page 1


27. Question
Evaluate the following integrals:
Answer
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:
Answer
We know that integration by parts is given by:
Page 2


27. Question
Evaluate the following integrals:
Answer
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:
Answer
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
Answer
Let 
Using integration by parts,
We know that,
Using integration by parts,
30. Question
Page 3


27. Question
Evaluate the following integrals:
Answer
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:
Answer
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
Answer
Let 
Using integration by parts,
We know that,
Using integration by parts,
30. Question
Evaluate the following integrals:
? sec
–1
 vx dx
Answer
Let 
dx=2tdt
Using integration by parts,
We know that, 
Substitute value for t,
31. Question
Evaluate the following integrals:
? sin
–1
 vx dx
Answer
Let 
dx=2tdt
Using integration by parts,
We know that,
Page 4


27. Question
Evaluate the following integrals:
Answer
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:
Answer
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
Answer
Let 
Using integration by parts,
We know that,
Using integration by parts,
30. Question
Evaluate the following integrals:
? sec
–1
 vx dx
Answer
Let 
dx=2tdt
Using integration by parts,
We know that, 
Substitute value for t,
31. Question
Evaluate the following integrals:
? sin
–1
 vx dx
Answer
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
Answer
Let 
Using integration by parts,
We know that,
33. Question
Page 5


27. Question
Evaluate the following integrals:
Answer
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:
Answer
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
Answer
Let 
Using integration by parts,
We know that,
Using integration by parts,
30. Question
Evaluate the following integrals:
? sec
–1
 vx dx
Answer
Let 
dx=2tdt
Using integration by parts,
We know that, 
Substitute value for t,
31. Question
Evaluate the following integrals:
? sin
–1
 vx dx
Answer
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
Answer
Let 
Using integration by parts,
We know that,
33. Question
Evaluate the following integrals:
Answer
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
Answer
Let 
Using integration by parts,