INTEGRATION USING SUBSTITUION METHOD PRACTICE WORKSHEET

Integrate the following :

(1)  cos x/(1+sin x) dx       Solution

(2)  ∫ [(6x + 5)/√(3x²+5x+6)] dx        Solution

(3)  ∫ cosec x dx       Solution

(4)  ∫ x⁵ (1 + x⁶)⁷ dx        Solution

(5)  (2Lx + m)/(Lx² + mx + n)    Solution

(6)  ∫(4ax+2b)/(ax2+bx+c)10 dx     Solution

(7)  ∫cos14 x sin x  dx      Solution

(8)  ∫sin5 x  dx      Solution

(9)   ∫ cos⁷x dx        Solution

(10)  (1 + tan x)/(x + log sec x)         Solution

(11)  ∫e^(m tan-1x)/(1+x²) dx         Solution

(12)   ∫x sin-1 (x2)/√(1 - x4) dx        Solution

(13)  ∫5 (x+1) (x+log x)4/x dx       Solution

(14)  ∫sin (log x)/x dx         Solution

(15)  ∫cot x/log sin x dx        Solution

(16)  ∫ sec4xtan x dx       Solution

(17)  ∫tan³x sec x dx         Solution

(18)  ∫ sin (x+a-a)/sin (x + a) dx         Solution

(19)  cos22 x- sin 6 x

(20)  1/(1+sin x)

(21)  1/(1-cos x)

(22)  √(1 - sin2x)

(23)  cos x/cos (x - a)

(24)  √tan x/sin x cos x

(25)  sin √x/√x

(26)  sin 2x/(a cos2x + b sin2x)

(27)  sin23 x + 4 cos 4 x

Answer

(1)  log (1+sin x) + C

(2)   2 √(3x2+5x+6) + C

(3)  log (cosec x - cot x) + C

(4)  (1 + x⁶)⁸/48 + C

(5)  log (Lx² + mx + n) + C

(6)  [-2/9(ax2+bx+c)9] + C

(7)  (1/15) sin15 x + C

(8)  (1/5)cos5x + (2/3)cos3x - cos x + C

(9)  sin x - sin3x+ (3/5)sin5x - (1/7) sin7x + C

(10) log (x + log sec x) + C

(11)  e^(m tan-1x)/m + C

(12)  (1/4) [sin-1 (x2)]2 + C

(13)  (x + log x)5 + C

(14)  cos (log x) + C 

(15)  log (log sin x) + C

(16)  (sec 4 x/4) + C

(17)  (sec3x/3) - sec x + C

(18)   cos ax - sin a log sin (x+a) + C

(19)  (1/2) [x + (sin 2x/2)] + (cos 6 x/6) + C

(20)  tan x - sec x + C

(21)  -cot x -cosec x + C

(22)  sin x + cos x + C

(23)   x cos a - sin a log cos (x-a) + C

(24)  2√tan x + C

(25)  -2cos √x + C

(26)   1/(b-a) ln (a cos2x + b sin2x) + C

(27)  (1/2)[x - (sin 6x/6)] + sin 4 x + C

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