Question

integration of sin cube x into sin 2x DX

Answer 1

integration of sin cube x into sin 2x dx=

we can write;

sin cube x= sinx into sin square x

sin2x= 2sinx cosx

= integration of  sinx. sin square x. 2 sinx. cosx

=2 (integration of sin square x. sin square x. cos x)

= 2 ( integration of sin power 4 x. cos x)......1 eqn

here;

let sin x = z

-cos x dx= dz

cos x dx= -dz

putting these value in eqn...1

= -2 ( integration of z power 4 dz)

= -2 [z power5 /5]

-2/5. sin power5 x..........ans......