The integrals below involve `e^(ax)`
1) `int e^(ax) dx = e^(ax)/a`
2) `int x*e^(ax) dx = e^(ax)/a(x-1/a)`
3) `int x^2e^(ax) dx = e^(ax)/a(x^2-(2x)/a+2/a^2)`
4) `int x^n*e^(ax) dx = (x^n*e^(ax))/a-n/aint x^(n-1)*e^(ax) dx`
`=e^(ax)/a(x^n-(nx^(n-1))/a+(n(n-1)x^(n-2))/a^2-...((-1)^n*n!)/a^n)`.....**If `n=`a positive integer**
5) `int e^(ax)/x dx = lnx+(ax)/(1*1!)+(ax)^2/(2*2!)+(ax)^3/(3*3!)+...`
6) `int e^(ax)/x^n dx = (-e^(ax))/((n-1)x^(n-1))+a/(n-1)int e^(ax)/x^(n-1) dx`
7) `int 1/(p+qe^(ax)) dx = x/p-1/(ap)ln(p+q e^(ax))`
8) `int 1/(p+qe^(ax))^2 dx = x/p^2+1/(ap(p+qe^(ax)))-1/(ap^2)ln(p+qe^(ax))`
9) `int 1/(pe^(ax)+qe^(-ax)) dx = 1/(asqrt(pq)) tan^-1(sqrt(p/q)*e^(ax))`
OR `= 1/(2asqrt(-pq)) ln ((e^(ax)-sqrt(-q/p))/(e^(ax)+sqrt(-q/p)))`
10) `int e^(ax) sin bx dx = (e^(ax)(a sin bx-b cos bx))/(a^2+b^2)`
11) `int e^(ax) cos bx dx = (e^(ax)(a cos bx+b sin bx))/(a^2+b^2)`
12) `int x e^(ax) sin bx dx = (x e^(ax)(a sin bx-b cos bx))/(a^2+b^2)-(e^(ax)[(a^2-b^2) sin bx+2ab cos bx])/(a^2+b^2)^2`
13) `int x e^(ax) cos bx dx = (x e^(ax)(a cos bx+b sin bx))/(a^2+b^2)-(e^(ax)[(a^2-b^2) cos bx+2ab sin bx])/(a^2+b^2)^2`
14) `int e^(ax) ln x dx = (e^(ax)ln x)/a-1/aint e^(ax)/x dx`
15) `int e^(ax) sin^n bx dx = (e^(ax)sin^(n-1)bx)/(a^2+n^2b^2)(a sin bx-nb cos bx)+(n(n-1)b^2)/(a^2+n^2b^2)int e^(ax) sin^(n-2)bx dx`
16) `int e^(ax) cos^n bx dx = (e^(ax)cos^(n-1)bx)/(a^2+n^2b^2)(a cos bx+nb sin bx)+(n(n-1)b^2)/(a^2+n^2b^2)int e^(ax) cos^(n-2)bx dx`