What is the antiderivative of (10 + x^2)/x^3. I keep coming up with an answer that is obviously wrong. And can you walk me through the steps? That would be greatly appreciated.
2006-11-24 04:21:54 · 6 answers · asked by Renee C 2 in Science & Mathematics ➔ Mathematics
Take the integral of this function, like this:
∫ (10 + x²) / x³ =
∫ (10 / x³) + ∫ (x² / x³) =
10 ∫ (1 / x³) + ∫ (1 / x) =
10 (-1 / 2x²) + ln(x) + C =
-5 / x² + ln(x) + C
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2006-11-24 04:36:08 · answer #1 · answered by I ♥ AUG 6 · 0⤊ 0⤋
Simplify it as 10/x^3 + 1/x
The answer is -5/x^2 + ln x
2006-11-24 12:47:03 · answer #2 · answered by ag_iitkgp 7 · 0⤊ 0⤋
Let y=(10 + x^2)/x^3
Integrating,
=>I=â«(10/x^3 + 1/x)dx
=>I=-5/x^2 + log|x| + C
2006-11-24 12:54:20 · answer #3 · answered by sushant 3 · 0⤊ 0⤋
AD of 10x^-3+1/x
=10x^-2/-2+logx+C
=-5/x^2+logx+C
2006-11-24 12:34:34 · answer #4 · answered by raj 7 · 0⤊ 0⤋
-5/x^2+ln(x)+c
2006-11-24 12:45:02 · answer #5 · answered by Muhammad 2 · 0⤊ 0⤋
integration
2006-11-24 12:31:24 · answer #6 · answered by Anonymous · 0⤊ 2⤋