Doug C. answered • 06/08/21
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Let u = x4 -4x2 - 9
du = (4x3- 8x)dx (this is convenient because it matches the numerator)
After substitution we have:
∫ du/√u = ∫ u-1/2 du
Which gives as an antiderivative:
2 u1/2 and after replacing u:
2(x4-4x2-9)1/2 + C (do not forget the constant of integration)
Patrick B.
The anti-derivative of U^k is [1/(k+1)]* U^(k+1) ; here k=-1/2; so the coefficient is 1/(-1/2+1) = 1/(1/2) = 2
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06/08/21
Doug C.
Another way to say it in words: to find the antiderivative of u^k (k a constant), raise the exponent by 1 then multiply by the reciprocal of the new exponent.
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06/08/21
Shin U.
Good day, sir! may i ask where did you get the 2?06/08/21