find the integration of the following question
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∫dx/√-2(x²+x+2)
add and sub half of coefficient of x
∫dx/√-2(x²+x+(1/2)²-(1/2)²+2)
completing square
∫dx/√-2[(x+1)²+7/4
∫dx/√[(√7/2)²-(x+1)²
using formula
∫dx√a²-x² = sin⁻¹(x/a)+C
=sin⁻¹[2(x+1)/√7]+C
where C is constant of integration
add and sub half of coefficient of x
∫dx/√-2(x²+x+(1/2)²-(1/2)²+2)
completing square
∫dx/√-2[(x+1)²+7/4
∫dx/√[(√7/2)²-(x+1)²
using formula
∫dx√a²-x² = sin⁻¹(x/a)+C
=sin⁻¹[2(x+1)/√7]+C
where C is constant of integration
heartking:
sorry wrong answer
yes little error
on place of (x+1 ), (x+ 1/2) =(2x+1) should written
(2x+1)/2
ya now correct
in answer, (x+1) replaces (2x+1)/2 and also divided by 2
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use identity :sin(inverse of) x/a + c
First split that equation into sum or differentce of two squares (completing the square) then use identity.
Ans: 1/root2 sin^(4x-2/root17)
First split that equation into sum or differentce of two squares (completing the square) then use identity.
Ans: 1/root2 sin^(4x-2/root17)
sorry wrong answer
What?
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