∫ sec³x dx

evaluate ∫ (sin 3x)^4 dx with limits 0 to pi



evaluate ∫ (sin 3x)^4 dx with limits 0 to pi

first express it as (sin
²3x)² then use trigonometry formula   to
express sin ²3x as (1-cos6x) /2
use (a-b)² identity to expand the numerator
again use trigonometry formula  to simplify cos ²6x
then integrate term by term using integration formula

 integral of fourth power of sin3x)with
                limits 0 to pi


evaluate ∫ sec³x dx
Take the integral as I
sec³x into secx *sec²x
note that
sec²x has a simpler integral tanx
than secx , choose
sec²x as the second function
and start using integration by parts
you will get an integral containing tan
which can be changed to
sec²x - 1
trigonometry formula .
Now split the integral into two , one of
which will be I
solve for the integral I.

integral of cube of

integral of cube of secx cube

other questions and problems:

*integral calculus integration formula

trigonometric identity and ratio of  certain standard angles

*list of differentiation formula     *integral calculus integration formula
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