WHICH o : (sin 3x.cos 6x dx.
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Step-by-step explanation:
ANSWER
∫sin
3
cos
3
xdx
=∫sin
3
x(1−cos
2
x)cosxdx
=∫sin
3
(1−sin
2
x)cosxdx
=∫sin
3
xcosxdx−∫sin
5
xcosxdx
Let sinx=t
On differentiating, we get
cosxdx=dt
Substituting the above variables
=∫t
3
dt−∫t
5
dt
=
4
t
4
−
6
t
6
+c
Re-substituting t=sinx, we get
=
4
sin
4
x
−
6
sin
6
x
+c.
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