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Integral of (x^3.^root(4x-x^2) dx with integral limits 0,4 Integral of x^4/(1+x^2)^4 dx with integral limits 0,5 pls giv me solution for above 2 questns in detailled steps

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\[\int x^{3}\sqrt{x^{2}-4} dx\]
Is that the integral?
I mean: \[\large \int\limits x^{3}\sqrt{4x-x^{2}} dx\]?

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Other answers:

Yes limits given in questn
Pls giv me slution in steps as i need to note it
i think you're supposed to do completing the swuare here
well, it's completing the square first then trig-sub. Why not you try it; then me typing the solution for you?
than me*
I dont know how to do,pls giv me steps
\[4x - x^2 = -(x^2 - 4x)\]\[= -(x^2 - 4x) - 4 + 4\]\[= -(x^2 - 4x + 4) + 4\]\[= 4 - (x^2 - 4x + 4)\]\[= 4 - (x - 2)^2\]\[\int\limits x^3 \sqrt{4x - x^2}dx = \int\limits x^3 \sqrt{4 - (x - 2)^2} dx\]there i already completed the square for you, just do trig subs and you'll be fine

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