求不定积分： | a^2x dx

求不定积分题见附件！求助做题要有详细过

(1) ∫[x*x^(1/3)]dx =∫[x^(4/3)]dx =(3/7)*x^(7/3)+C (2) ∫[(x^2/2)-(2/x^2)]dx =∫(x^2/2)dx-∫(2/x^2)dx =(1/6)*x^3+(2/x)+C (3) ∫[x^(1/2)+1]*[x^(3/2)-1]dx =∫[x^2-x^(1/2)+x^(3/2)-1]dx =∫x^2dx-∫x^(1/2)dx+∫x^(3/2)dx-∫dx =(1/3)x^3-(2/3)*x^(3/2)+(2/5)*x^(5/2)-x+C (4) ∫e^(5t)dt =(1/5)∫e^(5t)d(5t) =(1/5)*e^(5t)...全部

  (1) ∫[x*x^(1/3)]dx =∫[x^(4/3)]dx =(3/7)*x^(7/3)+C (2) ∫[(x^2/2)-(2/x^2)]dx =∫(x^2/2)dx-∫(2/x^2)dx =(1/6)*x^3+(2/x)+C (3) ∫[x^(1/2)+1]*[x^(3/2)-1]dx =∫[x^2-x^(1/2)+x^(3/2)-1]dx =∫x^2dx-∫x^(1/2)dx+∫x^(3/2)dx-∫dx =(1/3)x^3-(2/3)*x^(3/2)+(2/5)*x^(5/2)-x+C (4) ∫e^(5t)dt =(1/5)∫e^(5t)d(5t) =(1/5)*e^(5t)+C (5) ∫(3-2x)^3dx =(-1/2)∫(3-2x)^3d(3-2x) =(-1/2)*(1/4)*(3-2x)^4+C =(-1/8)*(3-2x)^4+C (6) ∫[1/(1-2x)]dx =(-1/2)∫[1/(1-2x)]d(1-2x) =(-1/2)*ln|1-2x|+C (7) ∫xcos(x^2)dx =(1/2)∫cos(x^2)d(x^2) =(1/2)sin(x^2)+C (8) ∫xe^(-x^2)dx =(-1/2)∫e^(-x^2)d(-x^2) =(-1/2)e^(-x^2)+C (9) ∫cos^3 xdx =∫cos^2 x*cosxdx =∫cos^2 xd(sinx) =∫(1-sin^2 x)d(sinx) =sinx-(1/3)sin^3 x+C (10) ∫(sinx/cos^3 x)dx =-∫(1/cos^3 x)d(cosx) =(1/2)*(1/cos^2 x)+C =(1/2)sec^2 x+C (11) ∫1/[e^x+e^(-x)]dx =∫[e^x/(e^2x+1)]dx =∫[1/(e^2x+1)]d(e^x) =arctan(e^x)+C。
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