1/(x^1/4+x^1/2)dx=

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/04/27 18:45:04

1/(x^1/4+x^1/2)dx=

∫1/(x⁴+x²+1) dx
= (1/2)∫(x+1)/(x²+x+1) dx - (1/2)∫(x-1)/(x²-x+1) dx
= (1/2)[(1/2)∫(2x+1)/(x²+x+1) dx + (1/2)∫1/(x²+x+1) dx]
- (1/2)[(1/2)∫(2x-1)/(x²-x+1) dx - (1/2)∫1/(x²-x+1) dx]
= (1/4)∫d(x²+x+1)/(x²+x+1) - (1/4)∫d(x²-x+1)/(x²-x+1)
+ (1/4)∫d(x+1/2)/[(x+1/2)²+3/4] + (1/4)∫d(x-1/2)/[(x-1/2)²+3/4]
= (1/4)ln|(x²+x+1)/(x²-x+1)| + (2/√3)arctan[(2x+1)/√3] + (2/√3)arctan[(2x-1)√3] + C

∫（x^2+1/x^4)dx ∫1/(x^4-x^2)dx ∫ x/(1+X^2)dx= ∫(x^4-4x^2+5x-15)/(x^2+1)(x-2) dx=? 1/(x^1/4+x^1/2)dx= 不定积分 [1/(e^x+e^(-x))]dx=?根号{[(x^2)-1]/x}dx=? ∫(1-x)/[√(9-4x^2)]dx= 求不定积分 ∫ [(x^4)/(1+x^2)]dx= ∫dx/（1+√(1-x^2)）=? ∫tan^4(x)dx=? ∫（(x+2)/4x(x^2-1)）dx 积分∫x/[(x^2+1)(x^2+4)]dx ∫(3x^4+x^2)/(x^2+1)dx