Integration - Chennai Tuition Centre,Home tuition in chennai Chennai Tuition Centre

u dv = uv -∫v du (Integration by parts)

a dx = ax + c where a is constant

xn dx = xn+1 / n+1 + c

ex dx = ex + c

1/x dx = log x + c

1/ x2 dx = - 1/x + c

Sin x dx = - Cos x + c

Cos x dx = Sin x + c

Sin ax dx = - Cos ax /a + c

Cos ax dx = Sin ax /a + c

Tan x Sec x dx = Sec x + c

Sec2 x dx = Tan x + c

Cosec2 x dx = - Cot x + c

Cot x Cosec x dx = - Cosec x + c

∫ √x dx = x3/2 / 3/2 + c

1/x dx = 2x + c

Tan x dx = log Sec x + c

Sec x dx = log (Sec x + Tan x) + c

Cosec x dx = - log (Cosec x + Cot x) + c

x dy + y dx = xy + c

Cot x dx = = log Sin x + c

∫ dx/√ (a2 - x2) = Sin-1 x/a + c

∫ dx/√ (a2 + x2) = log(x + √ (a2 + x2)) + c

∫ dx/√(x2 - a2) = Cos-1 x/a + c or log(x + √(x2 - a2)) + c

∫ dx/( a2 + x2) = 1/a Tan-1 x/a + c

∫ dx/( a2 - x2) = 1/2a log((a+x)/(a-x)) + c

∫ dx/(x2 - a2) = 1/2a log((x-a)/(x+a)) + c

∫ √ (a2 - x2) dx = x/a √ (a2 - x2) + a2/2 Sin-1 x/a + c

∫ √ (a2 + x2) dx = x/2 √ (a2 + x2) + a2/2 log(x + √ (a2 + x2)) + c

∫ √(x2 - a2) dx = x/2 √(x2 - a2) - a2/2 log(x + √(x2 - a2)) + c

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