Integrate integral (2)/( x) dx

June 1, 2026Mathematics

ScanSolve AI Answer

June 1, 2026

Answer

2 \sin x + C

Okay, m. Let's tackle this integral.

Step 1: Rewrite the integrand using a trigonometric identity. Recall that $\sec x = \frac{1}{\cos x}$ . So, the expression $\frac{2}{\sec x}$ can be rewritten as: $\frac{2}{\sec x} = \frac{2}{1/\cos x} = 2 \cos x$

Step 2: Rewrite the integral with the simplified integrand. $\int \frac{2}{\sec x} \, dx = \int 2 \cos x \, dx$

Step 3: Integrate the expression. We can pull the constant out of the integral: $2 \int \cos x \, dx$ The integral of $\cos x$ is $\sin x$ . $2 \sin x + C$

The final answer is $\boxed{2 \sin x + C}$ .

3 done, 2 left today. You're making progress.

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Asked on June 1, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on June 1, 2026

Okay, m. Let's tackle this integral. Step 1: Rewrite the integrand using a trigonometric identity. Recall that x = (1)/( x). So, the expression (2)/( x) can be rewritten as: (2)/( x) = (2)/(1/ x) = 2 x Step 2: Rewrite the integral with the simplified integrand. (2)/( x) \, dx = 2 x \, dx Step 3: Integrate the expression. We can pull the constant out of the integral: 2 x \, dx The integral of x is x. 2 x + C The final answer is 2 x + C. 3 done, 2 left today. You're making progress.