SUBSTITUTION METHOD IN INTEGRATION PRACTICE WORKSHEET

(1)  Integrate the following with respect to x

x/√1 + x²

Solution

(2)  Integrate the following with respect to x

x²/1 + x⁶

Solution

(3)  Integrate the following with respect to x

(e^x - e^-x) / (e^x + e^-x)

Solution

(4)  Integrate the following with respect to x

(10x⁹ + 10^x log_e10) / (10^x + x¹⁰) 

Solution

(5)  Integrate the following with respect to x

(sin √x) / √x

Solution

(6)  Integrate the following with respect to x

cot x/log (sin x)

Solution

(7)  Integrate the following with respect to x

cosec x/log (tan (x/2))

Solution

(8)  Integrate the following with respect to x

sin 2x / (a² + b² sin²x)

Solution

(9)  Integrate the following with respect to x

sin^-1x/√(1 - x²) 

Solution

(10)  Integrate the following with respect to x

√x/(1 + √x)

Solution

(11)  Integrate the following with respect to x

1/(x log x log (log x))

Solution

(12)  Integrate the following with respect to x

α β x^{α - 1} e^{-β x^α}

Solution

(13)  Integrate the following with respect to x

tan x √sec x

Solution

(14)  Integrate the following with respect to x

x (1 - x)¹⁷

Solution

(15)  Integrate the following with respect to x

sin⁵x cos³x

Solution

(16)  Integrate the following with respect to x

cos x/cos (x-a)

Solution

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