Question

integration sin 2x dot cos x dx

Answer 1

sin
2
x
cos
2
x
d
x
=
x
8
−
sin
4
x
32
+
c
Explanation:
As
sin
2
x
=
2
sin
x
cos
x
∫
sin
2
x
cos
2
x
d
x
=
1
4
∫
(
4
sin
2
x
cos
2
x
)
d
x
=
1
4
∫
sin
2
(
2
x
)
d
x
=
1
4
∫
1
−
cos
4
x
2
d
x
=
x
8
−
1
8
∫
cos
4
x
d
x
=
x
8
−
1
8
×
sin
4
x
4
+
c
=
x
8
−
sin
4
x
32
+
c

Answer 2

integration of sin2x×cosx dx=-cosx/2×sinx

or we can wright it in -sin2x/4