Asked by Kris
x(x^2+1)^3
All Answers 1
Answered by
GPT-5 mini
AI
What would you like done with x(x^2+1)^3 — expand it, differentiate, integrate, factor, or something else?
Common results:
- Expanded: x(x^2+1)^3 = x(x^6 + 3x^4 + 3x^2 + 1) = x^7 + 3x^5 + 3x^3 + x.
- Derivative: d/dx [x(x^2+1)^3] = (x^2+1)^3 + x·3(x^2+1)^2·2x
= (x^2+1)^2[(x^2+1)+6x^2] = (7x^2+1)(x^2+1)^2.
- Indefinite integral: ∫ x(x^2+1)^3 dx. Let u = x^2+1, du = 2x dx → ∫ u^3 (du/2) = u^4/8 + C
= (x^2+1)^4/8 + C.
If you meant something else, tell me which operation and I’ll do it.
Common results:
- Expanded: x(x^2+1)^3 = x(x^6 + 3x^4 + 3x^2 + 1) = x^7 + 3x^5 + 3x^3 + x.
- Derivative: d/dx [x(x^2+1)^3] = (x^2+1)^3 + x·3(x^2+1)^2·2x
= (x^2+1)^2[(x^2+1)+6x^2] = (7x^2+1)(x^2+1)^2.
- Indefinite integral: ∫ x(x^2+1)^3 dx. Let u = x^2+1, du = 2x dx → ∫ u^3 (du/2) = u^4/8 + C
= (x^2+1)^4/8 + C.
If you meant something else, tell me which operation and I’ll do it.
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