Question

evaluate the integral
∫x^2 cos2x dx

Answer 1

integration by parts

Answer 2

\[\int\limits x^2 \cos (2 x) \, dx=\frac{1}{2} x^2 \sin (2 x)-\int\limits x \sin (2 x) \, dx\]

Answer 3

integration by parts again
\[\frac{1}{2} x^2 \sin (2 x)+\frac{1}{2} x \cos (2 x)-\frac{1}{2}\int\limits \cos (2 x) \, dx\]

Answer 4

for cos2x , substitution
u=2x , du=2dx
\[\frac{1}{2} x^2 \sin (2 x)+\frac{1}{2} x \cos (2 x)-\frac{1}{4}\int\limits \cos (u) \, du\]

Answer 5

actually the question jst says evaluate the integral nt intergration by parts

Answer 6

integrate\[ x^2 \sin (x) \cos (x)-\frac{1}{4} \sin (2 x)+\frac{1}{2} x \cos (2 x)+c\]

Answer 7

evaluate=integrate?

Answer 8

thats jst what it said...-_-, cud u show the steps, please?

Answer 9

those are the steps

Answer 10

thanx :)

Answer 11

welcome