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−cosx+12+c\frac{-\cos x+1}{2}+c2−cosx+1+c
−3cos2x−12+c\frac{-3\cos2x-1}{2}+c2−3cos2x−1+c
14(sin2x+4cos2x−2x)+c\frac{1}{4}\left(\sin2x+4\cos2x-2x\right)+c41(sin2x+4cos2x−2x)+c
14(sin2x−4cos2x−2x)+c\frac{1}{4}\left(\sin2x-4\cos2x-2x\right)+c41(sin2x−4cos2x−2x)+c
−1-1−1
−13\frac{-1}{3}3−1
12\frac{1}{2}21
111
2x+10+c2x+10+c2x+10+c
x4+153x+c\frac{x^4+15}{3x}+c3xx4+15+c
x3+5x+cx^3+\frac{5}{x}+cx3+x5+c
2x+5x+c2x+\frac{5}{x}+c2x+x5+c
x23−4x+c\frac{x^2}{3}-4x+c3x2−4x+c
2x+c2x+c2x+c
x33−x2+4x+c\frac{x^3}{3}-x^2+4x+c3x3−x2+4x+c
x33+x2+4x+c\frac{x^3}{3}+x^2+4x+c3x3+x2+4x+c
∞\infty∞
000
14\frac{1}{4}41
444
116\frac{11}{6}611
666
275\frac{27}{5}527
295\frac{29}{5}529
16π16\pi16π
75π4\frac{75\pi}{4}475π
20π20\pi20π
81π4\frac{81\pi}{4}481π
(a)
令 u=x+1 ,求∫−13 xx+1 dx 的值 。令\ u=x+1\ ,求\int_{-1}^{3\ }\ x\sqrt{x+1\ }dx\ \ \ 的值\ 。令 u=x+1 ,求∫−13 xx+1 dx 的值 。 (a)
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