更新1:
let u = x^3+2x du = (3x^2)dx next = ?
Evaluate the indefinite integral (x^2+1)(x^3+2x)^4 dx?
回答 (2)
2016-05-29 5:05 pm
∫(x² + 1) (x³ + 2x)⁴ dx
= ∫(x² + 1) [(x³)⁴ + 4(x³)³(2x) + 6(x³)²(2x)² + 4(x³)(2x)³ + (2x)⁴] dx
= ∫(x² + 1) (x¹² + 8x¹⁰ + 24x⁸ + 32x⁶ + 16x⁴) dx
= ∫[(x¹⁴ + 8x¹² + 24x¹⁰ + 32x⁸ + 16x⁶) + (x¹² + 8x¹⁰ + 24x⁸ + 32x⁶ + 16x⁴)] dx
= ∫(x¹⁴ + 9x¹² + 32x¹⁰ + 56x⁸ + 48x⁶ + 16x⁴) dx
= (x¹⁵/15) + (9x¹³/13) + (32x¹¹/11) + (56x⁹/9) + (48x⁷/7) + (16x⁵/5) + C
= ∫(x² + 1) [(x³)⁴ + 4(x³)³(2x) + 6(x³)²(2x)² + 4(x³)(2x)³ + (2x)⁴] dx
= ∫(x² + 1) (x¹² + 8x¹⁰ + 24x⁸ + 32x⁶ + 16x⁴) dx
= ∫[(x¹⁴ + 8x¹² + 24x¹⁰ + 32x⁸ + 16x⁶) + (x¹² + 8x¹⁰ + 24x⁸ + 32x⁶ + 16x⁴)] dx
= ∫(x¹⁴ + 9x¹² + 32x¹⁰ + 56x⁸ + 48x⁶ + 16x⁴) dx
= (x¹⁵/15) + (9x¹³/13) + (32x¹¹/11) + (56x⁹/9) + (48x⁷/7) + (16x⁵/5) + C
2016-05-29 4:00 pm
Hint: Expand the binomial.
收錄日期: 2021-04-18 14:53:03
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https://hk.answers.yahoo.com/question/index?qid=20160529075641AAMYPxB