Anti derivative of $$1(x+a)(x+b)dx$$ is equal to

Correct option is 3logx+a+b2+x2+a+bx+ab+k

Questions

$Anti derivative of \frac{1}{\sqrt{(x + a) (x + b)}} d x is equal to$

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logx+a+b2+x2+a+bx−ab+k

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logx−a+b2+x2+a+bx+ab+k

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detailed solution

Correct option is C

I=∫dxx+ax+bI=∫dxx2+(a+b)x+abI=∫dxx2+2(a+b)2x+ab+a+b22−a+b22I=∫dxx+a+b22+4ab−(a+b)24I=∫dxx+a+b22−a−b22I=log⁡x+a+b2+x2+(a+b)x+ab+k

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Anti derivative of 1(x+a)(x+b)dx is equal to

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$Anti derivative of \frac{1}{\sqrt{(x + a) (x + b)}} d x is equal to$