Question
Mathematics Question on Integrals of Some Particular Functions
∫sinxcosx1 dx is equal to
A
log∣tanx∣+C
B
log∣sin2x∣+C
C
log∣secx∣+C
D
log∣cosx∣+C
Answer
log∣tanx∣+C
Explanation
Solution
Let I=∫(sinxcosxsin2x+cos2x)dx
=∫(sinxcosxsin2x+sinxcosxcos2xdx)
=∫(tanx+cotx)dx
=logsecx+(−logcosecx)+C
=logcosecxsecx+C=log∣tanx∣+C