SOLUTION: By a change of variables, determine the indefinite integral as follows: integral (x^2 - 3x^4)^1/2 dx The answer is supposed to be: (- (1 - 3x^2)^3/2) / 9 help me please

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: By a change of variables, determine the indefinite integral as follows: integral (x^2 - 3x^4)^1/2 dx The answer is supposed to be: (- (1 - 3x^2)^3/2) / 9 help me please      Log On


   

Question 565519: By a change of variables, determine the indefinite integral as follows:
integral (x^2 - 3x^4)^1/2 dx
The answer is supposed to be: (- (1 - 3x^2)^3/2) / 9
help me please
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
By a change of variables, determine the indefinite integral as follows:
integral (x^2 - 3x^4)^1/2 dx
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The integrand can be factored as:
sqrt%28x%5E2%281+-+3x%5E2%29%29+=+x%2Asqrt%281-3x%5E2%29
Let y+=+1+-+3x%5E2
Then dy+=+-6x%2Adx
So the integral can be written as
%28-1%2F6%29%2Aint%28y%5E%281%2F2%29%2Cdy%29
The antiderivative of %28-1%2F6%29y%5E%281%2F2%29+=+%28-1%2F6%29%282%2F3%29%2Ay%5E%283%2F2%29
Substituting back the expression for y gives
-%281-3x%5E2%29%5E%283%2F2%29%2F9