Indefinite Integrals

Easymathematics

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

Select the correct option:

$e^{x} ln x + C$

$e^{x} / x + C$

$e^{x} x ln x + C$

$e^{x} (1 + ln x) + C$

🔒 Solution Hidden from View

Submit your answer to unlock the detailed step-by-step solution.

About This Question

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

Solution

Correct Answer:

$e^{x} ln x + C$

Simplify the integrand: $\frac{1 + x l n x}{x} = \frac{1}{x} + ln x$ .
Recognize the standard form $\int e^{x} (f (x) + f^{'} (x)) d x = e^{x} f (x)$ . Let $f (x) = ln x$ . Then $f^{'} (x) = 1/ x$ .
The integral becomes: $\int e^{x} (ln x + \frac{1}{x}) d x = e^{x} ln x + C$ .

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

Looking for more practice? Explore all mathematics questions or browse integral calculus questions on RankGuru.

Indefinite Integrals

Select the correct option:

Solution

🔒 Solution Hidden from View

More indefinite integrals Practice Questions

Find the indefinite integral of the function 1 divided by the product x times the natural logarithm ...

The integral ∫sin(x) dx equals

The integral ∫(1/x) dx equals

The integral ∫x² dx equals

The integral ∫eˣ dx equals

About This Question

Solution