If ∫ cos x log(tan (x/2))dx = sin x log(tan (x/2))+ f(x) then f(x) is equal to, (assuming c is a arbitrary real constant)

Question

If ∫ cos x log(tan (x/2))dx = sin x log(tan (x/2))+ f(x) then f(x) is equal to, (assuming c is a arbitrary real constant) (A) c (B) c - x (C) c + x (D) 2x + c

Tardigrade Admin · Accepted Answer

IBP ⇒ I = sinx log(tan (x/2))-x + c ∴ f(x) = c - x

Q. If $\int cos x l o g (t an \frac{x}{2}) d x = s in x l o g (t an \frac{x}{2}) +$ f(x) then f(x) is equal to, (assuming c is a arbitrary real constant)

c

c - x

c + x

2x + c

$I BP \Rightarrow I = s in x l o g (t an \frac{x}{2}) - x + c$
$∴ f (x) = c - x$

Q. If ∫cosxlog(tan2x​)dx=sinxlog(tan2x​)+ f(x) then f(x) is equal to, (assuming c is a arbitrary real constant)

c

c - x

c + x

2x + c

IBP⇒I=sinxlog(tan2x​)−x+c ∴f(x)=c−x

Q. If $\int cos x l o g (t an \frac{x}{2}) d x = s in x l o g (t an \frac{x}{2}) +$ f(x) then f(x) is equal to, (assuming c is a arbitrary real constant)

$I BP \Rightarrow I = s in x l o g (t an \frac{x}{2}) - x + c$
$∴ f (x) = c - x$