Basics (not really though)
Repeated IBP
Cyclic Integrals
Definite Integrals
Harder stuff, probably...
100

Evaluate ∫ln⁡(x) dx

What is xln⁡(x)−x+C?

100

Evaluate ∫xexdx

What is xe^x−e^x+C or e^x(x−1)+C?

100

Evaluate ∫e^xsin(x)dx

What is (e^x(sinx−cosx))/2+C?

100

Evaluate ∫1->e(ln(x)dx)

What is 1?

100

Evaluate ∫x^2arctan(x)dx

What is (x^3/3)arctan(x)−6x^2+6ln(1+x^2)+C?

200

Evaluate ∫xln⁡(x) dx

What is (x^2/2)ln(x)-(x^2/4)+C? 

200

Evaluate ∫xcos(x)dx

What is xsin(x)+cos(x)+C?

200

Evaluate ∫e^xcos(x)dx

What is (e^x(sinx+cosx))/2+C 

200

∫0->1(xln(x)dx)

What is -1/4?

200

Evaluate ∫xln(x+1)dx 

What is (x^2-1/2)ln(x+1)−/4x^2+x/2+C ?

300

Evaluate ∫arctan⁡(x) dx

What is xarctan⁡(x)−12ln⁡(1+x^2)+C?

300

Evaluate ∫x^2e^xdx

What is e^x(x^2−2x+2)+C 

300

Evaluate ∫e^−xsin(x)dx 

What is −(e^−x(sinx+cosx))/2+C 

300

∫0->π(xsin(x)dx)

What is pi or π?

300

Evaluate ∫x^2ln^2(x)dx

What is (x^3/3)ln^2(x)−(2x^3/9)ln(x)+(2x^3/27)+C ?

400

Evaluate ∫ln⁡(2x+1) dx

What is (((2x+1)ln⁡(2x+1)−(2x+1))/2)+C?

400

Evaluate ∫x^3sin(x)dx

What is −x^3cos(x)+3x^2sin(x)+6xcos(x)−6sin(x)+C?

 

400

Evaluate ∫e^2xcos(3x)dx

(e^(2x)(2cos(3x)+3sin(3x)))/13+C

400

Evaluate ∫1->e(xln(x)dx)

What is (e^2+1)/4?

400

Evaluate ∫x^3e^xsin(x)dx

What is (e^x/2)[(x^3−3x^2+3x+3)sin(x)−(x^3+3x^2−3x−3)cos(x)]+C? (jeez man)

500

Evaluate ∫ln^⁡2(x) dx

What is x(ln^⁡2(x)−2ln(⁡x)+2)+C?

500

Evaluate ∫x^4e−xdx

−e^−x(x^4+4x^3+12x^2+24x+24)+C

500

Evaluate ∫e^(3x)sin(4x)dx

(e^(3x)(3sin(4x)−4cos(4x)))/25+C

500

Evaluate ∫0->π(x^2sin(x)dx)

What is π^2-4?

500

Evaluate ∫x

What is 1/2x^2? (Haha, I tricked you it wasn't actually that hard)

M
e
n
u