Can anyone take the integral of: x^2/(x^3)+4) dx?
Thanks
2007-05-10 09:21:03 · 4 answers · asked by Miami_Tennis 2 in Science & Mathematics ➔ Mathematics
Sure! Make a substitution u = x³+4, du = 3x² dx
and we get
1/3*∫ du/u = 1/3 ln |u| = 1/3*ln |x³+4| + C.
2007-05-10 09:27:10 · answer #1 · answered by steiner1745 7 · 0⤊ 0⤋
You have an extra close bracket. I assume your question is integral of [ (x^2) / ((x^3) + 4) ] dx.
Notice that the numerator is just one degree lower than the denominator.
= Integral of 1/3 [ (3x^2) / ((x^3) + 4) ] dx
Notice that, ignoring the 1/3 on the outside, the numerator is the differentiation of the denominator.
= 1/3 ln |(x^3) + 4| + C
2007-05-10 16:32:56 · answer #2 · answered by Kimbia 2 · 0⤊ 0⤋
You have unbalanced brackets, and these appear to have led to different interpretations.
Int x^2 dx / ( x^3 + 4 )
= d(x^3) / 3( x^3 + 4 )
= (1/3) log( x^3 + 4 ) + const.
2007-05-10 16:29:20 · answer #3 · answered by Anonymous · 0⤊ 0⤋
(1/3)ln(X^3)+4X
2007-05-10 16:28:19 · answer #4 · answered by erwins57 2 · 0⤊ 0⤋