Integration by Substitution (inc Trig Sub)
Integration by Parts
Fun with Trig
Definite Integrals
Rational Functions
100
4x^3 / sqrt(x^4 + 9)
2 sqrt(x^4 + 9) + C
100
x e^x
x e^x - e^x + C
100
(sin x) * cos (cos x)
-sin (cos x) + C
100
cos x from a = 0 to b = pi/2
1
100
1 / (3x + 2)
1/3 ln abs (3x + 2) + C
200
tan x (sec x)^4
1/4 (sec x)^4 + C or 1/4 (tan x)^4 + 1/2 (tan x)^2 + C
200
x ln x
1/2 x^2 ln x - 1/4 x^2 + C
200
sin x / cuberoot(cos x)
-3/2 cuberoot( (cos x)^2 ) + C
200
(x + 2x^2) / x from a = 1 to b = 2
4
200
x / (4x^2 + 1)
1/8 ln abs(4x^2 + 1) + C
300
1 / ( x sqrt (ln x) )
2 sqrt (ln x) + C
300
arctan x
x arctan x - 1/2 ln (1 + x^2) + C
300
(sin x)^2
1/2 x - 1/4 sin 2x + C
300
1 / (x ln x) from a = e to b = e^2
ln 2
300
(2x + 6) / ( x (x + 2) )
3 ln abs(x) - ln abs (x + 2) + C
400
x sqrt (x - 5)
2/5 (x-5)^(5/2) + 10/3 (x-5)^(3/2) + C
400
(x^2) (cos x)
(x^2) (sin x) - 2 sinx + 2x cos x + C
400
(tan x)^2 * (sec x)^4
1/5 (tan x)^3 (sec x)^2 + 2/15 (tan x)^3 + C or 1/5 (tan x)^5 - 1/3 (tan x)^3 + C
400
x e^x from a = 0 to b = 2
e^2 + 1
400
1 / (10x^2 + 10)
1/10 arctan x + C
500
sqrt (16 - x^2)
1/2 x sqrt (16 - x^2) + 8 arcsin (x/4) + C
500
e^sqrt(x)
2e^sqrt(x) sqrt(x) - 2e^sqrt(x) + C
500
(1 + cos x) / sin x Hint: Multiply top and bottom by (1 - cos x)
ln abs(1 - cos x) + C
500
1 / [ (x^2) sqrt(x^2 - 9) ] from a = 3 to b = 3sqrt(2)
sqrt(2) / 18
500
(5x + 23) / (x^2 + 8x +16)
5 ln abs(x + 4) - 3 / (x + 4) + C
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