Question

Hi please do this int

Answer 1

\[\int\limits_{}^{}dx/(\sin ^{4}x+\cos^{4}x)\]

Answer 2

it's very long to solve on here.

the way to do it is to multiply it by \[\frac{ \sec^4(x) }{ \sec^4(x) }\] to put it in a more manageable form.

i got this answer on wolfram; and you can click show step-by-step solution to see a way to solve it: http://www.wolframalpha.com/input/?i=integrate+1%2F%28sin^4%28x%29+%2B+cos^4%28x%29%29

who's giving you such hard integrals to solve? lol

Answer 3

it was a test exam

Answer 4

the link won't work. but you should type in wolfram with brackets to see it.

links cant have brackets so it's impossible to copy/paste it properly

Answer 5

so how could I answer this question in about 2 min ?

Answer 6

multiply it through by sec^4(x)/sec^4(x)

change a sec^2(x) in the numerator for (tan^2(x) + 1) itll be \[\frac{ \sec^{2}x(\tan^{2}x +1) }{ \tan^{4}x + 1 }\]

let u = tanx --> du = sec^2(x)

you'll then need to use partial fractions, have fun :P

Answer 7

integrals end up being ugly requiring square completion.

what class is this?

how evil is the teacher?

Answer 8

thank you for response I think it takes a lot to salve such int

Answer 9

yes. it does. the partial fraction decomposition isn't even obvious.

it ends up being: \[\frac{ A }{ (x^{2} + 2\sqrt{x} + 1) } + \frac{ B }{ x^{2} + 2\sqrt{x} - 1) }\]