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integral

∫ sec³x dx

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

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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

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problem2

evaluate ∫ sec³x dx
Take the integral as I
break
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
²x
which can be changed to
sec²x - 1
using
trigonometry formula .
Now split the integral into two , one of
which will be I
solve for the integral I.

integral of cube of
                secx

integral of cube of secx cube

other questions and problems:


*integral calculus integration formula





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trigonometric identity and ratio of  certain standard angles

*list of differentiation formula     *integral calculus integration formula
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