CA Foundation · Quantitative Aptitude · Differential and Integral Calculus
Evaluate ∫ (1/x + e^x + 2) dx, where C is the constant of integration.
The integral equals log x + e^x + 2x + C. Each term is integrated separately: 1/x gives the natural logarithm, e^x stays e^x, and the constant 2 becomes 2x. The constant of integration is added once at the end.
- Alog x + e^x + 2x + CCorrect
- B−1/x² + e^x + 2x + C
- Clog x + e^x + 2 + C
- Dx log x + e^x + 2x + C
Explanation
Integrate term by term: ∫(1/x)dx = log x, ∫e^x dx = e^x, ∫2 dx = 2x. So the result is log x + e^x + 2x + C. The option with −1/x² wrongly differentiates 1/x instead of integrating it, and the option ending in 2 + C forgets to integrate the constant.
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