∫ xⁿ dx = x⁽ⁿ ⁺ ¹⁾/(n + 1) + c
∫ (1/xⁿ) dx = -1/(n - 1) x⁽ⁿ⁻¹⁾ + c
∫ (1/x) dx = log x + c
∫ e^(x) dx = e^x + c
∫ a^(x) dx = a^x/(log a) + c
∫ sin x dx = - Cos x + c
∫ cos x dx = Sin x + c
∫ cosec ² x dx = - Cot x + c
∫ sec² x dx = tan x + c
∫ sec x tan x dx = sec x + c
∫ cosec x cot x dx = - cosec x + c
∫ 1/(1 + x²) dx = tan ⁻ ¹x + c
∫ 1/ √(1 - x²) dx = sin ⁻ ¹x + c
∫ tan x dx = log |sec x| + c
∫cot x dx = log |sin x| + c
∫cosec x dx = log |cosec x - cot x| + c
∫sec x dx = log |sec x + tan x| + c
∫u dv = uv - ∫vdu
Bernoulli formula :
∫u dv = uv - u'v1 + u''v2 - ............
∫f'(x)/f(x) dx = log |x| + c
∫ f'(x) [f(x)]n dx = [f(x)]n + 1/(n + 1)
∫e(a x + b) dx = (1/a)e(a x + b) + c
∫(ax + b)ⁿdx = (1/a)(ax + b)(n + 1)/(n + 1) + c
∫1/(ax + b)dx = (1/a)log(ax + b) + c
∫sin (ax + b)dx = -(1/a)cos(ax + b) + c
∫cos (ax + b)dx = (1/a)sin(ax + b) + c
∫sec2(ax + b)dx = (1/a)tan(ax + b) + c
∫cosec2(ax + b)dx = -(1/a)cot(ax + b) + c
∫cosec(ax+b)cot(ax+b)dx = -(1/a)cosec (ax+b) + c
∫sec(ax + b)tan (ax + b)dx = sec(ax + b) + c
∫1/[1 + (ax)2]dx = (1/a)tan-1(ax) + c
∫1/ √[1 - (ax)2] dx = (1/a) sin-1(ax) + c
∫ eax sin bx dx = eax/(a2 + b2) (a sin bx - b cos bx) + c
∫ eax cos bx dx = eax/(a2 + b2) (a cos bx + b sin bx) + c
∫ dx/(a2-x2) = (1/2a) log [(a + x)/(a - x)] + c
∫ dx/(x2-a2) = (1/2a) log [(x - a)/(x + a)] + c
∫ dx/(a2+ x2) = (1/a) tan-1 (x/a) + c
∫ dx/(√a2- x2) = sin-1 (x/a) + c
∫ dx/(√x2- a2) = log (x + (√x2- a2)) + c
∫ dx/(√x2+ a2) = log (x + (√x2+ a2)) + c
∫ √(a2- x2) = (x/2) √(a2- x2) + (a2/2) sin-1(x/a) + c
∫ √(x2- a2) = (x/2) √(x2- a2) - (a2/2) log(x+√(x2- a2))+c
∫ √(x2+a2) = (x/2) √(x2+ a2) + (a2/2) log(x+√(x2+ a2))+c
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