Basic Integration Rules

BASIC RULES

100

∫ (4x^3 + x^2 + 3)dx

x^4 + (x^3\ 3x) + 3x + C

200

∫ (1/X^3) dx

(-1/2x^2) + C

300

∫ 6x(x-1) dx

2x^3 - 3x^2 + C

400

∫ ((2x^3 + 1) / x^3) dx

2x - (1/2x^2) + C

500

∫ (14x^6 - 256x^3 + 2187x^2+ 1024x) dx

2x^7 + 64x^4 + 729x^3 + 512x^2 + C

U-SUBSTITUTION

100

∫ 2(1 + 2x)^4 dx

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

200

∫ (x(x^2 - 1)^7) dx

(((x^2 - 1)^8)/16) + C

300

∫ (-3/(√(2x + 3 ))) dx

-3(2x+3)^1/2 + C

400

∫ (6x/(1 + (x^2)^3) dx

-3/(2(1 + x^2)^2)) + C

500

∫ ((3x^2 + 7x + 4) / (x^3 + 4x^2 + 4x)) dx

ln|x| + 2ln|x+2|+ (1/(x+2))

LOG RULES

100

∫ (1/(x+1)) dx

ln|x+1| + C

200

∫ (1/(3-2x)) dx

(-1/2)ln|3-2x| + C

300

∫(2/(3x + 5)) dx

(2/3)ln|3x + 5| + C

400

∫(1/(6x - 5)) dx

(1/6) ln|6x - 5| + C

500

∫ (5/(2x-1)) dx

(5/2) ln|2x-1| + C