Question

i need help in definite integration

Answer 1

\[\int\limits_{0}^{1} x^4(1-x^4)/(1+x^2)\]

Answer 2

first factor 1 - x^4
= (1 - x^2)(1 + x^2)

this will simpl ify your expression

Answer 3

sorry it is (1-x)^4 not (1-x^4)

Answer 4

\[\large \rm \int\limits_{0}^{1} \dfrac{x^4(1-x)^4}{1+x^2}~dx\]

Answer 5

yes i forgot dx too...

Answer 6

Nice pic @panchajanya

Answer 7

i would expand (1-x)^4, there could be some other clever trick though

Answer 8

\[\rm \begin{align} \dfrac{x^4(1-x)^4}{1+x^2} &= \dfrac{x^4(x^4-4x^3+6x^2-4x+1)}{1+x^2}\\~\\
&=\dfrac{x^4\left[x^4 -4x(1+x^2) + 6(1+x^2)-5\right]}{1+x^2}\\~\\
& = \dfrac{x^4(x^4-5)}{1+x^2} - 4x^5 + 6x^4\\~\\
& = \cdots
\end{align}\]

Answer 9

@iGreen

Answer 10

@thomaster

Answer 11

you could do long division on the first term
this will give
x^6 - x^4 - 4x^2 + 4 - 4 /(1 + x^2)
so substituting for the first term we get:-
x^6 - 4x^5 + 5x^4 - 4x^2 + 4 - 4/(1+x^2)

so integrate term by term - the last term is a standard integral - if my memory serves me right the integral is -4 arctan x