The value of the integral e^x (1/x - 1/x^2) dx is : Option 1: e^x/x + c Option 2: (e^(-x))/x + c Option 3: e^x + C Option 4: e^(-x) + C

Answer: e^x/x + c. Solution: Using the standard result e^x [f(x) + f'(x)] dx = e^x f(x) + c. Let f(x) = 1/x, so f'(x) = -1/x^2. Then e^x (1/x - 1/x^2) dx = e^x * 1/x + c = e^x/x + c.

Applied Mathematics

Calculus

Easy

The value of the integral $\int e^x \left(\frac{1}{x} - \frac{1}{x^2}\right) dx$ is :

$\frac{e^x}{x} + c$

$\frac{e^{-x}}{x} + c$

$e^x + C$

$e^{-x} + C$

✅ Correct Option: 1

Using the standard result $\int e^x [f(x) + f'(x)] dx = e^x f(x) + c$ .

Let $f(x) = \frac{1}{x}$ , so $f'(x) = -\frac{1}{x^2}$ .

Then $\int e^x \left(\frac{1}{x} - \frac{1}{x^2}\right) dx = e^x \cdot \frac{1}{x} + c = \frac{e^x}{x} + c$ .

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The total cost function for $x$ units of a commodity is given by $C(x) = \frac{25x^3}{3} - 75x^2 + 48x + 34$ . The output $x$ at which the marginal cost is minimum is :

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The value of the integral ∫ex(1x−1x2)dx\int e^x \left(\frac{1}{x} - \frac{1}{x^2}\right) dx∫ex(x1​−x21​)dx is :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The value of the integral $\int e^x \left(\frac{1}{x} - \frac{1}{x^2}\right) dx$ is :