x^8(10+x^9)^3 Calculate the indefinite integral?
回答 (4)
2020-08-07 2:25 am
✔ 最佳答案
x^8 * (10 + x^9)^3 * dxu = 10 + x^9
du = 9x^8 * dx
(1/9) * 9 * x^8 * dx * (10 + x^9)^3 =>
(1/9) * du * u^3 =>
(1/9) * u^3 * du
Integrate
(1/9) * (1/4) * u^4 + C =>
(1/36) * (10 + x^9)^4 + C
2020-08-07 2:54 am
Let u = 10 + x⁹
Then, du = 9x⁸dx, and thus x⁸dx = (1/9)du
∫ x⁸ (10 + x⁹)³ dx
= ∫ (10 + x⁹)³ (x⁸dx)
= (1/9) ∫ u³ du
= (1/9) (1/4) u⁴ + C
= (1/36)(10 + x⁹)⁴ + C
Then, du = 9x⁸dx, and thus x⁸dx = (1/9)du
∫ x⁸ (10 + x⁹)³ dx
= ∫ (10 + x⁹)³ (x⁸dx)
= (1/9) ∫ u³ du
= (1/9) (1/4) u⁴ + C
= (1/36)(10 + x⁹)⁴ + C
2020-08-07 3:47 am
J = Int'l of x^8(10+x^9)^3dx.;
Put u = 10+x^9. Then du/dx = 9x^8, ie., (1/9)du=(x^8)dx & J=(1/9)Int'l(u^3du)
= (1/36)u^4 + c, where c is an arbitrary constant of integration. Then indefinite
integral is (1/36)(10+x^9)^4 + c.
Put u = 10+x^9. Then du/dx = 9x^8, ie., (1/9)du=(x^8)dx & J=(1/9)Int'l(u^3du)
= (1/36)u^4 + c, where c is an arbitrary constant of integration. Then indefinite
integral is (1/36)(10+x^9)^4 + c.
2020-08-07 3:30 am
Guess and correct like this
Let y = (x^9 + 10)^4
dy/dx = 36x^8(x^9 + 10)^3
I = ∫x^8(10 + x^9)^3 dx = (1/36)(10 + x^9)^4 + C
Let y = (x^9 + 10)^4
dy/dx = 36x^8(x^9 + 10)^3
I = ∫x^8(10 + x^9)^3 dx = (1/36)(10 + x^9)^4 + C
收錄日期: 2021-04-18 18:36:05
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