**
Question 7
**

Find: ∫ (x
^{
2
}
+ sin
^{
2
}
โกx) sec
^{
2
}
โกx / (1 + x
^{
2
}
) dx

Last updated at Dec. 4, 2018 by Teachoo

**
Question 7
**

Find: ∫ (x
^{
2
}
+ sin
^{
2
}
โกx) sec
^{
2
}
โกx / (1 + x
^{
2
}
) dx

Transcript

Question 7 Find: โซ1โ((๐ฅ^2 + sin^2โก๐ฅ ) sec^2โก๐ฅ)/(1 + ๐ฅ^2 ) dx โซ1โ((๐ฅ^2 + sin^2โก๐ฅ ) sec^2โก๐ฅ)/(1 + ๐ฅ^2 ) dx = โซ1โ((๐ฅ^2 + sin^2โก๐ฅ )(1/cos^2โก๐ฅ ) )/(1 + ๐ฅ^2 ) dx = โซ1โ((๐ฅ^2 + sin^2โก๐ฅ ) )/((1 + ๐ฅ^2 ) cos^2โก๐ฅ ) dx Writing sin2 x = 1 โ cos2 x = โซ1โ((๐ฅ^2 + 1 โ cos^2โก๐ฅ ) )/((1 + ๐ฅ^2 ) cos^2โก๐ฅ ) dx = โซ1โ((1 + ๐ฅ^2 ) โ cos^2โก๐ฅ )/((1 + ๐ฅ^2 ) cos^2โก๐ฅ ) dx = โซ1โ((1 + ๐ฅ^2 ) )/((1 + ๐ฅ^2 ) cos^2โก๐ฅ ) dx โ โซ1โ(cos^2โก๐ฅ )/((1 + ๐ฅ^2 ) cos^2โก๐ฅ ) dx = โซ1โ1/cos^2โก๐ฅ dx โ โซ1โ(1 )/((1 + ๐ฅ^2 ) ) dx = โซ1โใ๐ ๐๐ใ^2โก๐ฅ dx โ โซ1โ(1 )/((1 + ๐ฅ^2 ) ) dx = ๐๐๐ ๐โใ๐๐๐ใ^(โ๐) ๐ + 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 You are here

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

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.