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Choose the correct option.
Evaluate: ∫ x/(x² + 1) dx
Evaluate: $\int \frac{x}{x^2 + 1}\,dx$
- (a)$2\log(x^2 + 1) + c$
- (b)$\frac{1}{2}\log(x^2 + 1) + c$
- (c)$e^{x^2 + 1} + c$
- (d)$\log x + \frac{x^2}{2} + c$
Answer
Answer
Correct option: (b)
Answer: (b) $\frac{1}{2}\log(x^2+1) + c$
Put $x^2+1 = t$, so $x\,dx = \frac{dt}{2}$.
$\int \frac{x}{x^2+1}dx = \frac{1}{2}\int\frac{dt}{t} = \frac{1}{2}\log(x^2+1) + c$.