Indefinite Integrals

Easymathematics

The integral ∫eˣ dx equals

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eˣ + C

xeˣ⁻¹ + C

eˣ/x + C

ln(x) + C

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Subject: mathematics
Chapter: integral calculus
Topic: indefinite integrals
Difficulty: Easy
Year: 2025

Solution

Correct Answer:

eˣ + C

Unique Property: The natural exponential function $f (x) = e^{x}$ is the only function (aside from zero) that acts as its own derivative and its own integral.
Relation: Since $\frac{d}{d x} e^{x} = e^{x}$ , the family of antiderivatives is $e^{x} + C$ .
Result: $\int e^{x} d x = e^{x} + C$ .

This easy difficulty mathematics question is from the chapter integral calculus, covering the topic of indefinite integrals. It appeared in the 2025 exam.

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Indefinite Integrals

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Solution

Indefinite Integrals

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Solution

Evaluate $\int e^{x} (\frac{1 + x l n x}{x}) d x$ (Assume $x > 0$ and base $e$ for $ln$ ).