definite integral

\int_{1}^{\infty}{\frac{x^3+3}{x^6(x^2+1)}} = ?

6 Answers

11
Mani Pal Singh ·

dude
replace x by 1/x

u will get

∫012x5(1+3x3)dx/1+x2

now put 1+x2=t

numerator ko aise hi t main bana lena
nicche waala t upper se kaat kar

ek simple polynomial ko integrate karna hoga

i hope u could solve the rest

1
Vivek ·

not zero,how can it be zero when the function is always positive in the given range?

1
°ღ•๓яυΠ·

i took x=tan@

so dx=sec^2@d@

limitz frm pi/4 to pi/2

u egt int of

cot^3@(1+3cot^3@)d@

1
Optimus Prime ·

lol

1
Vivek ·

thanks manipal,that substitution did the trick,also made the limits 0 to 1!!
!!
if u go the trig way ,u hit a dead end as shown above,thats what i was doing before !!

1
Optimus Prime ·

ans 9/2+log 2.

i have solved it completely but it is too lengthy to b posted. if it is right then the method i used is dividing the numerator and deno and then substituting it by other variable. use it n still if u can't get the ans then i'll post d solution.

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