Review

Integration by Parts

100

∫(xe^x)dx

(xe^x)-(e^x)+C

200

∫(xcos3x)dx

((1/3)xsin(3x))+((1/9)cos(3x))+C

300

∫(xsinx)dx

-xcosx+sinx+C

400

∫((x^2)(e^3x))dx

(x(5^x)/ln5)-((5^x)/(ln5)^2)+C

500

∫((e^x)cosx)dx

(1/2)((e^x)cosx+(e^x)sinx)+C

Rapid Repeated

100

∫x^4sinx dx

-24 cos(x)+12 x^2 cos(x)-x^4 cos(x)-24 x sin(x)+4 x^3 sin(x) +c

200

∫(x^2-5x)e^x dx

(x^2-7x+7)e^x + C

300

∫x^3lnx dx

.25x^4lnx-.0625x^4 + c

400

∫ x^5cosx dx

120 cos(x)-60 x^2 cos(x)+5 x^4 cos(x)+120 x sin(x)-20 x^3 sin(x)+x^5 sin(x) + c

500

∫ x^4e^-x dx

-e^(-x) (24+24 x+12 x^2+4 x^3+x^4) + c

Partial Fractions

100

∫[(4 11)/(x^2 + 5x - 14)]dx

(4/9)ln|x-2| - (4/9)ln|x+7| + C

200

∫[(3x + 11)/(x^2 - x - 6)]dx

4ln|x-3| - ln|x+2| + C

300

∫[(x^2 + 4)/(3x^3 + 4x^2 - 4x)]dx

-ln|x| + (1/2)ln|x+2| + (5/6)ln|3x-2| + C

400

∫[(3x^2 + 1)/(x^3 - 9x^2 + 15x + 25)]dx

(1/9)ln|x+1| + (26/9)ln|x-2| - (38/3)/(x-5) + C

500

∫[(6x^2 - 3x)/(x^2 + 2x - 8)]dx

6x + 3ln|x-2| - 18ln|x+4| + C