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HOW TO INTEGRATE sin(ax+b) cos(ax+b)dx
Dear ABHISHEK VASHIST,
To integrate sin(ax+b) cos(ax+b),follwo these steps
let ax+b=t
then dx=dt/a
the expression is transformed to
1/a*(sin 2t).dt
integrating it we get
1/a*(-1/2)*(cos 2t) +c
Hope this helped you immensely...
All the Very Best & Good Luck to you ...
Regards,
AskIITians Expert,
Godfrey Classic Prince
IIT-Madras
Please approve my answer if you liked it by clicking on "Yes" given below...!!
for this apply fllowing sobstitution:i.e double substitution:
let, ax+b= t
then adx=dt
then,dx=dt/a
then,∫sin(t)cos(t)dt/a......1
then,1/a∫sin t cos t dt
now, cos(t)=z (suppose)
then, dcos (t)/dt= dz/dt
or, -sint = dz then substituting the value in 1,
we get ,-1/a ∫dz.z then by integrating, we get -z2/2a, now by putting the value we get, -cos(t)2/2a= -cos(ax+b)2/2a. if you like my answer plz approve!!!
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