Integration

Integration by parts

100

Using Integration by parts, solve: ∫xe^x dx

What is

 xe^x - e^x + C?

200

Using Integration by parts, solve: ∫ln⁡(x) dx

What is

xln⁡(x)−x+C?

300

Using Integration by parts, solve:∫xcos⁡(x) dx

What is 

xsin⁡(x)+cos⁡(x)+C?

400

Using Integration by parts, solve: ∫x^2 e^x dx

What is 

x^2 e^x−2xe^x+2e^x+C?

500

Using Integration by parts, solve: ∫e^x cos⁡(x) dx

What is 

(e^x (sin⁡(x)+cos⁡(x)))/2 +C?

Trig Integration

100

Using Trig Integration, solve: ∫sin⁡^2 (x) dx

What is 

x/2 - sin⁡(2x)/4 +C?

200

Using Trig Integration, solve: ∫cos⁡^3 (x) dx

What is 

sin⁡(x) − (sin⁡3(x)/3) +C?

300

Using Trig Integration, solve: ∫sec⁡(x) dx

What is 

ln ⁡|sec⁡(x)+tan⁡(x)| +C?

400

Using Trig Integration, solve: ∫tan⁡(x) dx

What is 

ln⁡ |sec⁡(x)| +C?

500

Using Trig Integration, solve: ∫sin⁡(x)cos⁡(x) dx

What is 

−cos⁡(2x)/4 +C?

Trig Substitution

100

Using Trig Substitution, solve: 

∫ sqrt(a^2−x^2) dx

What is 

a^2/2 arcsin⁡(x/a)+(x sqrt(a^2−x^2))/4+C

200

Using Trig Substitution, solve: ∫dx/ sqrt(a^2−x^2)

What is 

arcsin⁡(x/a)+C?

300

Using Trig Substitution, solve: ∫x^2+a^2 dx

What is

x sqrt(x^2+a^2)/2+ a^2/ 2ln⁡ ((sqrt(x^2+a^2) +x) −a^2/2ln⁡(a)+C?

400

DAILY DOUBLE!!!!

Using Trig Substitution, solve: ∫dx/x^2 sqrt(x^2−a^2)

What is

sqrt(x^2−a^2)/ax+C

500

Using Trig Substitution, solve: ∫x^2/a^2−x^2 dx

What is

a^2/2arcsin(a/x)−x sqrt(a^2−x^2)/4 +C?

Partial Fraction

100

Using Partial Fraction Integration, solve: 1/(x^2−1)

What is

1/2/x−1 + −1/2/x+1 = 1/2(1/x−1 − 1/x+1)?

200

Using Partial Fraction Integration, solve: x+3/x^2+2x

What is 

3/2 / x + 1/2 / x+2?

300

Using Partial Fraction Integration, solve: 

2x+5/ (x+1)(x^2+1)

What is 

1/x+1 + (x+4)/(x^2+1)?

400

Using Partial Fraction Integration, solve: (3x^2+5x+2)/(x^3−x)

What is 

1/x + 2/x−1?

500

Using Partial Fraction Integration, solve: (2x^2+3x+1)/((x−2)^2(x+1))

What is

1/(x−2) + 3/((x−2)^2) + 1/(x+1)?