Question

∫((1 + x)sinx)/((x² + 2x) cos² x – (1 + x)sin2x) dx = 

(a) (1/2) log |(sinx – (x + 1) cos x – 1)/(sinx – (x + 1)cos x + 1))| + c 

(b) (1/2) tan^–1{sinx – (x + 1) cos x} + c 

(c) (1/2) sin^–1{sinx – (x + 1) cos x} + c 

(d) (1/2) sin^–1(sinx + cos x) + c

Answer 1

Correct option is (a) (1/2) log |(sinx – (x + 1) cos x – 1)/(sinx – (x + 1)cos x + 1)| + c