poly integration

Wireless- SG

This qn is was asterisked. And as usual i cant do it .

quailmaster SG

try to complete the square to get a standard integration form, then refer to formula list

wee_ws SG

Hi,

Completing the square of a quadratic function is a very helpful skill to have.

When one encounters an expression like 1 / sqrt { f(x) }, where f(x) is a quadratic function, the result may be an inverse trigonometric (sine or cosine) or inverse hyperbolic (sine or cosine) expression.

If one sees an expression like f'(x) / sqrt { f(x) }, the result becomes 2 sqrt { f(x) } + c instead.

Thanks.

Cheers,
Wen Shih

Wireless- SG

how to complete that square.

sqrt[-x^2-4x]= sqrt[-1(x^2+4x)

=sqrt[-1 ((x+2)^2-4) ]

Then whata to do? Did i do it wrongly?

Wireless- SG

omg nvm got it. After that can jsut use the formulae. thanks!

wee_ws SG

Hi Wireless,

You could always consider

-x^2 - 4x = a - (x + b)^2,

where a and b are constants to be determined.

Thanks.

Cheers,
Wen Shih