The integrals below involve inverse trigonometric functions.
1) `int sin^-1 (x/a) dx = x*sin^-1 (x/a)+sqrt(a^2-x^2)`
2) `int x*sin^-1(x/a) dx = (x^2/2-a^2/4)sin^-1(x/a)+(xsqrt(a^2-x^2))/4`
3) `int x^2 sin^-1(x/a) dx = x^3/3sin^-1(x/a)+((x^2+2a^2)sqrt(a^2-x^2))/9`
4) `int (sin^-1(x/a))/x dx = x/a+(x/a)^3/(2*3*3)+(1*3(x/a)^5)/(2*4*5*5)+(1*3*5(x/a)^7)/(2*4*6*7*7)+...`
5) `int (sin^-1(x/a))/x^2 dx = -(sin^-1(x/a))/x-1/a ln((a+sqrt(a^2-x^2))/x)`
6) `int [sin^-1(x/a)]^2 dx = x[sin^-1(x/a)]^2-2x+2sqrt(a^2-x^2)*sin^-1(x/a)`
7) `int cos^-1(x/a) dx = x*cos^-1(x/a)-sqrt(a^2-x^2)`
8) `int x*cos^-1(x/a) dx = (x^2/2-a^2/4)cos^-1(x/a)-(xsqrt(a^2-x^2))/4`
9) `int x^2 cos^-1(x/a) dx = x^3/3 cos^-1(x/a)-((x^2+2a^2)sqrt(a^2-x^2))/9`
10) `int (cos^-1(x/a))/x dx = pi/2 lnx-int (sin^-1(x/a))/x dx`
**[See integral #4 in this table]
11) `int (cos^-1(x/a))/x^2 dx = -(cos^-1(x/a))/x+1/aln((a+sqrt(a^2-x^2))/x)`
12) `int [cos^-1(x/a)]^2 dx = x[cos^-1(x/a)]^2-2x-2sqrt(a^2-x^2) *cos^-1(x/a)`
13) `int tan^-1(x/a) dx = x*tan^-1(x/a)-a/2ln(x^2+a^2)`
14) `int x*tan^-1(x/a) dx = 1/2(x^2+a^2)tan^-1(x/a)-(ax)/2`
15) `int x^2*tan^-1(x/a) dx = x^3/3tan^-1(x/a)-(ax^2)/6+a^3/6ln(x^2+a^2)`
16) `int (tan^-1(x/a))/x dx = x/a-(x/a)^3/3^2+(x/a)^5/5^2-(x/a)^7/7^2+...`
17) `int (tan^-1(x/a))/x^2 dx = -1/xtan^-1(x/a)-1/(2a)ln((x^2+a^2)/x^2)`
18) `int cot^-1(x/a) dx = x*cot^-1(x/a)+a/2ln(x^2+a^2)`
19) `int x*cot^-1(x/a) dx = 1/2(x^2+a^2)cot^-1(x/a)+(ax)/2`
20) `int x^2 *cot^-1(x/a) dx = x^3/3cot^-1(x/a)+(ax^2)/6-a^3/6ln(x^2+a^2)`
21) `int (cot^-1(x/a))/x dx = pi/2lnx-int (tan^-1(x/a))/x dx`
**[See integral #16 in this table]
22) `int (cot^-1(x/a))/x^2 dx = -(cot^-1(x/a))/x+1/(2a)ln((x^2+a^2)/x^2)`
23) `int sec^-1(x/a) dx = x*sec^-1(x/a)-a ln(x+sqrt(x^2-a^2))`.....For `0 < sec^-1(x/a) < pi/2`
OR `= x*sec^-1(x/a)+a ln(x+sqrt(x^2-a^2))`.....For `pi/2 < sec^-1(x/a) < pi`
24) `int x*sec^-1(x/a) dx = x^2/2sec^-1(x/a)-(asqrt(x^2-a^2))/2`.....For `0 < sec^-1(x/a) < pi/2`
OR `= x^2/2sec^-1(x/a)+(asqrt(x^2-a^2))/2`.....For `pi/2 < sec^-1(x/a) < pi`
25) `int x^2*sec^-1(x/a) dx = x^3/3sec^-1(x/a)-(axsqrt(x^2-a^2))/6-a^3/6ln(x+sqrt(x^2-a^2))`.....For `0 < sec^-1(x/a) < pi/2`
OR `= x^3/3sec^-1(x/a)+(axsqrt(x^2-a^2))/6+a^3/6ln(x+sqrt(x^2-a^2))`.....For `pi/2 < sec^-1(x/a) < pi`
26) `int (sec^-1(x/a))/x dx = pi/2ln x+a/x+(a/x)^3/(2*3*3)+(1*3(a/x)^5)/(2*4*5*5)+(1*3*5(a/x)^7)/(2*4*6*7*7)+...`
27) `int (sec^-1(x/a))/x^2 dx = -(sec^-1(x/a))/x+sqrt(x^2-a^2)/(ax)`.....For `0 < sec^-1(x/a) < pi/2`
OR `= -(sec^-1(x/a))/x-sqrt(x^2-a^2)/(ax)`.....For `pi/2 < sec^-1(x/a) < pi`
28) `int csc^-1(x/a) dx = x*csc^-1(x/a)+a ln(x+sqrt(x^2-a^2))`.....For `0 < csc^-1(x/a) < pi/2`
OR `= x*csc^-1(x/a)-a ln(x+sqrt(x^2-a^2))`.....For `-pi/2 < csc^-1(x/a) < 0`
29) `int x*csc^-1(x/a) dx = x^2/2 csc^-1(x/a)+(asqrt(x^2-a^2))/2`.....For `0 < csc^-1(x/a) < pi/2`
OR `= x^2/2 csc^-1(x/a)-(asqrt(x^2-a^2))/2`.....For `-pi/2 < csc^-1(x/a) < 0`
30) `int x^2 csc^-1(x/a) dx = x^3/3csc^-1(x/a)+(axsqrt(x^2-a^2))/6+a^3/6ln(x+sqrt(x^2-a^2))`.....For `0 < csc^-1(x/a) < pi/2`
OR `= x^3/3csc^-1(x/a)-(axsqrt(x^2-a^2))/6-a^3/6ln(x+sqrt(x^2-a^2))`.....For `-pi/2 < csc^-1(x/a) < 0`
31) `int (csc^-1(x/a))/x dx = -(a/x+(a/x)^3/(2*3*3)+(1*3(a/x)^5)/(2*4*5*5)+(1*3*5(a/x)^7)/(2*4*6*7*7)+...)`
32) `int (csc^-1(x/a))/x^2 dx = -(csc^-1(x/a))/x-sqrt(x^2-a^2)/(ax)`.....For `0 < csc^-1(x/a) < pi/2`
OR `= -(csc^-1(x/a))/x+sqrt(x^2-a^2)/(ax)`.....For `-pi/2 < csc^-1(x/a) < 0`
33) `int x^m sin^-1(x/a) dx = x^(m+1)/(m+1)sin^-1(x/a)-1/(m+1) int x^(m+1)/sqrt(a^2-x^2) dx`
34) `int x^mcos^-1(x/a) dx = x^(m+1)/(m+1)cos^-1(x/a)+1/(m+1)int x^(m+1)/sqrt(a^2-x^2) dx`
35) `int x^mtan^-1(x/a) dx = x^(m+1)/(m+1)tan^-1(x/a)-a/(m+1)int x^(m+1)/(x^2+a^2) dx`
36) `int x^mcot^-1(x/a) dx = x^(m+1)/(m+1)cot^-1(x/a)+a/(m+1)int x^(m+1)/(x^2+a^2) dx`
37) `int x^msec^-1(x/a) dx = (x^(m+1)sec^-1(x/a))/(m+1)-a/(m+1)int x^m/sqrt(x^2-a^2) dx`.....For `0 < sec^-1(x/a) < pi/2`
OR `= (x^(m+1)sec^-1(x/a))/(m+1)+a/(m+1)int x^m/sqrt(x^2-a^2) dx`.....For `pi/2 < sec^-1(x/a) < pi`
38) `int x^mcsc^-1(x/a) dx = (x^(m+1)csc^-1(x/a))/(m+1)+a/(m+1)int x^m/sqrt(x^2-a^2) dx`.....For `0 < csc^-1(x/a) < pi/2`
OR `= (x^(m+1)csc^-1(x/a))/(m+1)-a/(m+1)int x^m/sqrt(x^2-a^2) dx`.....For `-pi/2 < csc^-1(x/a) < 0`