Integration

Integration by Parts

100

int(ln x) dx

What is x ln x - x+C

200

int(x e^x) dx

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

300

int( x^5 e^2x) dx

What is x^5 e^2x/2 - 5x^4 e^2x/4 + 5x^3 e^2x/2 - 15^x2 e^2x/4 + 15x e^2x/4 + C

400

int(e^x sin x) dx

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

500

int(sec^3 x) dx

What is (1/2) (sec x tan x + ln | sec x + tan x |) + C

Indefinite Integrals

100

int(5x+(2/3x^5)) dx

What is 5/2 x^2-(1/6x^4) + C

200

int(x^-3 - 3x^1/4 + 8x^2) dx

What is -1/2x^2 + 12/5 x^5/4 + 8/3 x^3 + C

300

int(x(1+x^2))dx

What is x^2/2 + x^5/5 + C

400

int(3sin(x) - 2sec^2(x))dx

What is -3cos(x)-2tan(x)+C

500

int(sec(x)/cos^2(x))dx

What is sec(x)+C

U Substitution

100

int(cos^3x sinx) dx

What is -(cos^4x/4)+C

200

int[from 0 to 2](-2x sq(4-x^2))dx

What is -16/3

300

int(e^x e^x)dx

What is e^2x/2

400

int( (2x+5)(x^2+5x)^7 )dx

What is (1/8)(x^2+5x)^8+C

500

int((3-x)^10) dx

What is (-1/11)(3-x)^11+C

Trigonometric Integrals

100

int(sin^3 x cos^2 x) dx

What is -(cos^3 x)/3 - (cos^5 x)/5 + C

200

int(sin^4 x cos^5 x) dx

What is (cos^5 x)/5 - 2 (cos^7 x)/7 + (cos^9 x)/9 + C

300

int(sec^4 x tan^2 x) dx

What is (tan^3 x)/3 - (tan^5 x)/5 + C

400

int(sec^3 x tan^5 x) dx

What is (sec^7 x)/7 - 2 (sec^5 x)/5 + (sec^3 x)/3 + C

500

int(cos^2 x sin^2 x) dx

What is 1/8 (x - 1/4 sin4x)+C

Partial Fraction Decomposition

100

3x/(2x+1)(x+4)

What is [-3/7(2x+1)]+[12/7(x+4)]

200

(x+5)/(x+3)^2

What is [1/(x+3)]+[2/(x+3)^2]

300

[(2x^2-3)/(x-1)^3(x+1)]

What is -1/8(x-1) + 9/4(x-1)^3 - 1/2(x-1)^3 + 1/8(x+1)

400

(x^3-2)/(x^4-1)

What is (x+2)/2(x^2+1) + 3/4(x+1) - 1/(4x-1)

500

1/x^2(x-2)

What is -1/4lnx+1/2x + 1/4ln(x-2)+K