Integration Methods

U-Sub

100

Evaluate ∫xcos(4x²)dx

⅛sin(4x²)+c

200

Evaluate ∫(x+1)/(½x²+x+2)dx

ln(½x²+x+2)+c

By Parts

100

Evaluate ∫2x³e^4xdx

(½)x³e^4x-(3/8)x²e^4x+(3/16)xe^4x-(3/64)e^4x+c

200

Evaluate ∫(4x)cos(2x)dx

(2x)sin(2x)+cos(2x)+C

Partial Fractions

100

Evaluate ∫ (7/(x²-5x+6))dx

7ln(x-3)-7ln(x-2)+c

200

Evaluate ∫ ⁸/(x³+2x²+x)dx

8(ln|x|-2ln|x+1|-(¹/[x-1])+c

Trig Subs

100

Evaluate ∫cos(x)sec²(sin(x))dx

tan(sin(x))+c

200

Evaluate ∫sin⁵(x)cos²(x)dx

((-cos⁷(x))/7)+((2cos⁵(x))/5)-((cos³(x))/3)+c

Improper Integrals

100

Evaluate ₂₇∫^∞ (3x^-4/3) dx

3

200

Evaluate ₂∫^10.5 (x²)+(²/_(x-3)) dx

Diverges