Question

sin³(2x + 1).dx
Integrate the function

Answer 1

HELLO DEAR,


Given function is integral of sin³(2x+1).dx

$\sf{\int{sin^2(2x+1)*sin(2x+1)}\,dx}$

$\sf{\int{[1 - cos^2(2x+1)]*sin(2x+1)}\,dx}$

let cos(2x+1) = t , dx=dt/-2sin(2x+1)

so, [tex]\sf{\int{[1-t^2]*sin(2x+1)*dt/-2sin(2x+
1)}\,dx}[/tex]

$\sf{-1/2\int{[1.dt-t^2.dt]}\,dx}$

$\sf{-1/2(t-t^3/3)+c}$

put the value of t in above function

[tex]\sf{\frac{-cos(2x+1)}{2}+\frac{cos^3(2x+1)}{6}+
c}[/tex]

I HOPE ITS HELP YOU DEAR,
THANKS