積分 求解啊，麻煩了

∫(x/5+4)^4dx=5∫(x/5+4)^4d(x/5+4)
=(x/5+4)^5+c

∫dx/[cos^2x(1+tanx)]
=∫dx/[cos^2x(cosx+sinx)/cosx]
=∫(cosx-sinx)/(cosxcos2x)dx
=∫dx/cos2x+∫dcosx/(2cos^3x-cosx)
=(1/2)∫d2x/cos2x+∫dX/X(2X^2-1)
=(1/2)ln|secx+tanx|-1/2ln(x^2/|2x^2-1|)+C
這里用到公式∫dx/[x(ax^2+b)]=[1/(2b)]*ln(x^2/|ax^2+b|)+C

∫xdx/√伍啟擾(-9x^2-6x),x<0,X^2=-x
=∫2X^3dX/X√(6-9X^2)
=∫2X^2dX/√(6-9X^2)
提腔旦出分母的9，利用公旁蠢式

∫x^2dx/√(a^2-x^2)=-x/2√(a^2-x^2)+(a^2/2)arcsin(x/a)+C
就OK了
符號(hào)太多了。。。。。。。。

10.: = -(log(cos(pi x+2)))/pi+constant

11.: = -2 log(sin((3-x)/2))+constant

12.: = -e^(cot(x))+constant

13.: = -(i (tan^(-1)((tan(x/2)-i)/sqrt(2))-tan^(-1)((tan(x/2)+i)/sqrt(2))))/sqrt(2)+constant

14.: = 2^(tan^(-1)(x))/(log(2))+constant

15.: = sin^(-1)(e^x/帶者2)+constant

16.: = (sin(x^5))/5+constant

17.: = (sqrt(3) x (3 x+2)-2 sqrt(x) sqrt(3 x+2) sinh^(-1)(sqrt(3/2) sqrt(x)))/(9 sqrt(-x (3 x+2)))+constant

18.: = 26/5 log(-x-4)+9/5 log(x-1)+constant

II.

1.: = e^(4 x) ((5 x)/4-13/16)+constant

2.: = 2/27 (9 x^2-8) sin((3 x)/遲陪2)+8/9 x cos((3 x)/2)+constant

3.: = -(3 (2 log(x)+3))/(4 x^(2/3))+constant

4.: = x cos^(-1)(5 x)-1/5 sqrt(1-25 x^2)+constant

5.: = 1/2 x^2 cot^(-1)(x)+x/2-1/2 tan^(-1)(x)+constant

III

1.: = 1/6 sqrt(1-36 x^2)+x sin^(-1)(6 x)+constant

2.: = 25/24 sin((3 x)/碼行蠢5)+25/144 sin((9 x)/5)+1/48 sin(3 x)+constant

3.: = (sec^5(x))/5-(2 sec^3(x))/3+sec(x)+constant

4.: = (sin(x))/2+1/14 sin(7 x)+constant

5.: = x-1/9 cot(3 x+5) (csc^2(3 x+5)-4)+5/3+constant