**
Question 19
**

Find: ∫ (x
^{
4
}
+ 1) / x (x
^{
2
}
+ 1)
^{
2
}
dx

Last updated at Dec. 11, 2018 by Teachoo

**
Question 19
**

Find: ∫ (x
^{
4
}
+ 1) / x (x
^{
2
}
+ 1)
^{
2
}
dx

Transcript

Question 19 Find: โซ1โ(๐ฅ^4 + 1)/(๐ฅ(๐ฅ^2 + 1)^2 ) dx โซ1โ(๐ฅ^4 + 1)/(๐ฅ(๐ฅ^2 + 1)^2 ) dx Writing x4 +1 = x4 + 1 + 2x2 โ 2x2 โซ1โ(๐ฅ^4 + 1)/(๐ฅ(๐ฅ^2 + 1)^2 ) dx = โซ1โ(๐ฅ^4 + 1 + 2๐ฅ^2 โ 2๐ฅ^2)/(๐ฅ(๐ฅ^2 + 1)^2 ) dx = โซ1โ((๐ฅ^2 + 1)^2 โ 2๐ฅ^2)/(๐ฅ(๐ฅ^2 + 1)^2 ) dx = โซ1โ(๐ฅ^2 + 1)^2/(๐ฅ(๐ฅ^2 + 1)^2 ) dx โ โซ1โ(2๐ฅ^2)/(๐ฅ(๐ฅ^2 + 1)^2 ) dx = โซ1โ1/๐ฅ dx โ โซ1โ2๐ฅ/(๐ฅ^2 + 1)^2 dx = logโกใ|๐ฅ|ใ โ โซ1โ2๐ฅ/(๐ฅ^2 + 1)^2 dx Let x2 + 1 = t 2x dx = dt = logโกใ|๐ฅ|ใ โ โซ1โ๐๐ก/๐ก^2 = logโกใ|๐ฅ|ใ โ ๐ก^(โ2 + 1)/(โ2 + 1) + C = logโกใ|๐ฅ|ใ โ ๐ก^(โ1)/(โ1) + C = logโกใ|๐ฅ|ใ + 1/t + C Putting back t = x2 + 1 = logโกใ|๐ฅ|ใ + 1/(x^2 + 1) + C

CBSE Class 12 Sample Paper for 2019 Boards

Paper Summary

Question 1

Question 2

Question 3

Question 4 (Or 1st)

Question 4 (Or 2nd)

Question 5

Question 6

Question 7

Question 8 (Or 1st)

Question 8 (Or 2nd)

Question 9

Question 10 (Or 1st)

Question 10 (Or 2nd)

Question 11

Question 12 (Or 1st)

Question 12 (Or 2nd)

Question 13 (Or 1st)

Question 13 (Or 2nd)

Question 14

Question 15

Question 16 (Or 1st)

Question 16 (Or 2nd)

Question 17

Question 18

Question 19 You are here

Question 20

Question 21 (Or 1st)

Question 21 (Or 2nd)

Question 22

Question 23

Question 24 (Or 1st)

Question 24 (Or 2nd)

Question 25

Question 26 (Or 1st)

Question 26 (Or 2nd)

Question 27 (Or 1st)

Question 27 (Or 2nd)

Question 28

Question 29

Class 12

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.