# Misc 11

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Misc 11 Integrate the function 1 cos 𝑥 + 𝑎 cos 𝑥 + 𝑏 𝑑𝑥 cos 𝑥 + 𝑎 cos(𝑥 + 𝑏) Divide & Multiplying by 𝐬𝐢𝐧 𝒂−𝒃 = sin 𝑎 − 𝑏 sin 𝑎 − 𝑏 × 1 cos 𝑥 + 𝑎 cos 𝑥 + 𝑏 𝑑𝑥 = 1 sin 𝑎 − 𝑏 sin 𝑎 − 𝑏 cos 𝑥 + 𝑎 cos 𝑥 + 𝑏 𝑑𝑥 = 1 sin 𝑎 − 𝑏 sin 𝑎 − 𝑏 + 𝑥 − 𝑥 cos 𝑥 + 𝑎 cos 𝑥 + 𝑏 𝑑𝑥 = 1 sin 𝑎 − 𝑏 sin ( 𝑥 + 𝑎 − 𝑥 + 𝑏) cos 𝑥 + 𝑎 cos 𝑥 + 𝑏 𝑑𝑥 = 1 sin 𝑎 − 𝑏 𝑠𝑖𝑛 𝑥 + 𝑎 𝑐𝑜𝑠 𝑥 + 𝑏 − 𝑐𝑜𝑠 𝑥 + 𝑎 𝑠𝑖𝑛 𝑥 + 𝑏 cos 𝑥 + 𝑎 cos 𝑥 + 𝑏 𝑑𝑥 = 1 sin 𝑎 − 𝑏 𝑠𝑖𝑛 𝑥 + 𝑎 𝑐𝑜𝑠 𝑥 + 𝑏 cos 𝑥 + 𝑎 cos 𝑥 + 𝑏 − cos 𝑥 + 𝑎 sin 𝑥 + 𝑏 cos 𝑥 + 𝑎 cos 𝑥 + 𝑏 𝑑𝑥 = 1 sin 𝑎 − 𝑏 𝑠𝑖𝑛 𝑥 + 𝑎 cos 𝑥 + 𝑎 − 𝑠𝑖𝑛 𝑥 + 𝑏 cos 𝑥 + 𝑏 𝑑𝑥 = 1 sin 𝑎 − 𝑏 tan 𝑥+𝑎 − tan 𝑥+𝑏 𝑑𝑥 Thus, our equation becomes 1 cos 𝑥 + 𝑎 cos 𝑥 + 𝑏 𝑑𝑥 = 1 sin 𝑎 − 𝑏 tan 𝑥+𝑎− tan 𝑥+𝑎 𝑑𝑥 = 1 sin 𝑎 − 𝑏 [− log cos 𝑥+𝑎+𝐶1− − log cos 𝑥+𝑏+𝐶2 = 1 sin 𝑎 − 𝑏 − log cos 𝑥+𝑎+ log cos 𝑥+𝑏+𝐶1+𝐶2 = 1 sin 𝑎 − 𝑏 − log cos 𝑥+𝑎+ log cos 𝑥+𝑏+ 𝟏 𝒔𝒊𝒏 𝒂 + 𝒃 𝑪𝟏+𝑪𝟐 = 1 sin 𝑎 − 𝑏 − log cos 𝑥+𝑎+ log cos 𝑥+𝑏+𝑪 = 𝟏 𝒔𝒊𝒏 𝒂 + 𝒃 𝐥𝐨𝐠 𝒄𝒐𝒔 𝒙 +𝒃 𝒄𝒐𝒔 𝒙 +𝒂+𝑪

Misc 1

Misc 2

Misc 3

Misc 4

Misc 5

Misc 6

Misc 7

Misc 8 Important

Misc 9

Misc 10

Misc 11 You are here

Misc 12

Misc 13

Misc 14

Misc 15

Misc 16

Misc 17

Misc 18 Important

Misc 19 Important

Misc 20 Important

Misc 21

Misc 22

Misc 23

Misc 24 Important

Misc 25

Misc 26

Misc 27

Misc 28

Misc 29

Misc 30 Important

Misc 31

Misc 32 Important

Misc 33

Misc 34

Misc 35

Misc 36

Misc 37

Misc 38

Misc 39

Misc 40

Misc 41 Important

Misc 42

Misc 43

Misc 44 Important

Integration Formula Sheet - Chapter 7 Class 12 Formulas Important

About the Author

CA Maninder Singh

CA Maninder Singh is a Chartered Accountant for the past 8 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .