INDEFINITE INTEGRALS & U-SUBSTITUTION

Indefinite Integrals

100

∫a^x dx

What is a^x/ln|a| + C

200

∫(t^2-sint)dt

What is t^3/3+cost+C

300

∫(4sinx+2cosx)dx

What is -4cosx+2sinx+C

400

∫(1-cscxcotx)dx

What is X+cscx+C

500

∫(x^3+x-2)/x^2 dx

What is x^2/2+lnlx|+(2x^-1)/(-1)+C

U-Substitution

100

∫0 dx

C

200

∫5cos5x dx

What is sin5x+C

300

∫2x(x^2+1)^23 dx

What is (x^2+1)^24)/24+

400

∫(tanx+3)secx^2 dx

What is (tanx+3)^2)/2+C

500

∫√(9-x^2) (-x)dx

What is 1/3 ((9-x^2)^3/2)+C

Constant Multiple Rule

100

∫sin(4x) dx

-cos(4x)/4 + C

200

∫(3x-1)^5 dx

What is ∫(3x-1)^6/18+C

300

∫sec^2(5x)dx

What is 1/5 tan(5x)+C

400

∫xsinx^2dx

What is -1/2 cos(x^2)+C

500

∫sec(4x)tan(4x)dx

What is 1/4 sec(4x)+C

e^power Rule

100

∫e^(-x) dx

-e^(-x) + C

200

∫e^(4x) dx

What is 1/4 e^(4x)+C

300

∫2x^3 e^(x^(4)) dx

What is (e^(x^4))/2+C

400

∫cos⊖e^sin⊖d⊖

What is e^(sin⊖)+C

500

∫e^4t (4+e^4t)^(−3) dt

(4+e^4t)^(−2)/-8+C

Natural Log Rule

100

∫13/(9+6x) dx

13/6 ln|9+6x| + C

200

∫dy/(y+5)

What is ln|y+5|+C

300

∫(e^x)/(2+e^x)dx

What is ln|2+e^x|+C

400

∫(e^x)/(5e^x+6) dx

What is 1/5 ln|5e^x+6|+C

500

∫(e^x-e^-x)/(e^x+e^-x)dx

What is ln|e^x+e^-x|+C