Integration of Parts

Trigonometric

100

xsin(x)

-xcos(x)+sin(x)+C

200

sin^2(x)

½(-sin(x)cos(x)+x)+C

300

x^2sin(x)

-x^2cos(x)+2xsin(X)+2cos(x)+C

400

xtan^2(x)

xtan(x)=ln|cos(x)|-½(x^2)+C

500

sec^3(x)

½(sec(x)tan(x))+½(ln|sec(x)+tan(x)|)+C

Logarithms

100

ln(x)

xln(x)-x+C

200

xln(x)

½(x^2)ln(x)-¼(x^2)+C

300

ln(x)^2

x(ln(x))^2-2xln(x)+2x+C

400

x^3ln(x)

ln(x)x^4 / x^4/16 +C

500

cos(x)ln(sin(x))

sin(x)ln(sin(x))-sin(x)+C

Exponential

100

xe^x

xe^x-e^x+C

200

(x^2)e^x

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

300

(x)e^2x

(xe^2x)/2-(e^2x)/4 + C

400

sin(x)e^x

½(e^x)[sin(x)-cos(x)]+C

500

cos(4x)e^3x

3/25(e^3x)[cos(4x)+4/3(sin(4x))]+C

Inverse Trigonometric (500 points each)

100

arccos(x)

x arccos(x) - sqrt(1-x^2) +C

200

arcsin(x)

x arcsin(x) + sqrt(1-x^2) + C

300

arctan(x)

xarctan(x) -½(ln(x^2+1)+C

400

xarccos(x)

(arccos(x)*x^2)/2 + arcsin(x)-x(sqrt(1-x^2)/4 +C

500

xarcsin(x)

(arcsin(x)x^2)/2 + (-arcsin(x)+ -x(sqrt(1-x^2)))/4 + C