SOLUTION: integrate (x ^ 2)/(x ^ 3 + 4) dx from 0 to 5 =

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Question 1198799: integrate (x ^ 2)/(x ^ 3 + 4) dx from 0 to 5 =

Answer by mccravyedwin(407) About Me  (Show Source):
You can put this solution on YOUR website!
int%28+%28x%5E2%29%2F%28x%5E3+%2B+4%29%2C+dx%2C0%2C5%29

Notice that the numerator has the same power of x, (2), as the derivative of
the denominator x%5E3%2B4 has. The derivative of the denominator is 3x%5E2.

So the numerator can be made into the derivative of the denominator by inserting
a 3 factor in the numerator and multiplying by 1/3 on the outside of the
integral sign.

expr%281%2F3%29int%28+%283x%5E2%29%2F%28x%5E3+%2B+4%29%2C+dx%2C0%2C5%29

We use the formula int%28du%2Fu%29%22%22=%22%22ln%28u%29%22%22%2B%22%22C

expr%281%2F3%29ln%28x%5E3%2B4%29matrix%283%2C1%2C%22%7C5%22%2C%22%7C++%22%2C%22%7C0%22%29%22%22=%22%22expr%281%2F3%29%28ln%285%5E3%2B4%29-ln%280%5E3%2B4%29%5E%22%22%29%22%22=%22%22expr%281%2F3%29%28ln%28129%29-ln%284%29%5E%22%22%29.

That is approximately 1.157839348

Edwin