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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