The GATE Grind

GATE 2022 CE (CE2) – Question 12

Engineering Mathematics · Calculus: Integrals, partial and total derivatives, gradient, divergence, curl, line, surface and volume integrals · 1 mark · Multiple choice

Evaluate $\int\left(x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+\cdots\right)dx$.

  1. $1/(1+x)+C$
  2. $1/(1+x^2)+C$
  3. $-1/(1-x)+C$
  4. $-1/(1-x^2)+C$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) $1/(1+x)+C$

Explanation

The displayed series is $\log(1+x)$ for $|x|<1$. Integrating by parts gives $\int\log(1+x)dx=(1+x)\log(1+x)-x+C$.

**None of the printed options equals this antiderivative.** For example, differentiating option A gives $-1/(1+x)^2$, not the displayed series. A is retained only as a provisional database choice pending source review.