integration of {2t+3 ÷ 7t + 22} dt
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Given : {(2t+3) ÷( 7t + 22)} dt
To Find : integrate
Solution:
(2t + 3)/ ( 7t + 22)
= 7(2t + 3)/7(7t + 22)
= (14t + 21 )/ 7(7t + 22)
= ( 14t + 44 + 21 - 44) / 7(7t + 22)
= ( 14t + 44 -23 ) / 7(7t + 22)
= (14t + 44)/7(7t + 22) - 23/7(7t + 22)
= 2/7 - 23/7(7t + 22)
(2/7)∫ dt - (23/7)∫ dt/(7t + 22)
= 2t/7 - (23/7) ln | 7t + 22 | / 7 + C
= 2t/7 - 23 ln | 7t + 22 | /49 + C
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