INTEGRATION BY DECOMPOSITION WORKSHEET

(1)  Integrate the following functions with respect to x :

(x³ + 4x² - 3x + 2)/x²              Solution

(2)  Integrate the following functions with respect to x :

(√x + (1/√x))²            Solution

(3)  Integrate the following functions with respect to x :

(2x - 5)(36 + 4x)            Solution

(4)  Integrate the following functions with respect to x :

(cot²x + tan²x)             Solution

(5)  Integrate the following functions with respect to x :

(cos 2x - cos 2a) / (cos x - cos a)            Solution

(6)  Integrate the following functions with respect to x :

cos 2x/(sin²x cos²x)      Solution

(7)  Integrate the following functions with respect to x :

(3 + 4cos x)/sin²x      Solution

(8)  Integrate the following functions with respect to x :

sin²x / (1 + cos x)      Solution

(9)  Integrate the following functions with respect to x :

sin 4x/sin x      Solution

(10)  Integrate the following functions with respect to x :

cos 3x cos 2x       Solution

(11)  Integrate the following functions with respect to x :

sin² 5x            Solution

(12)  Integrate the following functions with respect to x :

(1 + cos 4x) / (cot x - tan x)          Solution

(13)  Integrate the following functions with respect to x :

e^{x log a} e^x                Solution

(14)  Integrate the following functions with respect to x :

(3x + 4)√(3x + 7)               Solution

(15)  Integrate the following functions with respect to x :

(8^{1 + x} + 4^{1- x}) / 2^x               Solution

(16)  Integrate the following functions with respect to x :

1/(√(x + 3) - √(x + 4))               Solution

(17)  Integrate the following functions with respect to x :

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

(18)  Integrate the following functions with respect to x :

1/(x - 1) (x + 2)²           Solution

(19)  Integrate the following functions with respect to x :

(3x - 9)/(x - 1)(x + 2)(x² + 1)          Solution

(20)  Integrate the following functions with respect to x :

x³/(x - 1)(x - 2)          Solution

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