Evaluate: \(\int\frac{3x^2}{1 + x^3}dx\)

1.	Evaluate: \(\int\frac{3x^2}{1 + x^3}dx\)
Answer» \(\int\frac{3x^2}{1 + x^3}dx\) = log(1 + x³)+c or using \(\int\frac{f'(x)}{f(x)}dx\) logf(x) + c put 1 + x³ = t ∴ 3x²dx = dt ∴ = ∫ \(\frac{1}{t}\)dt = log t + c = log(1 + x³) + c

Answer»

\(\int\frac{3x^2}{1 + x^3}dx\) = log(1 + x³)+c or using

\(\int\frac{f'(x)}{f(x)}dx\) logf(x) + c

put 1 + x³ = t

∴ 3x²dx = dt

∴ = ∫ \(\frac{1}{t}\)dt = log t + c = log(1 + x³) + c

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