Published by:
CGP EDU Academic Team
Published on: September 12, 2026
Find the value of 
.
Text Solution
Verified by ExpertsThe correct answer is:
A
To evaluate the integral \(\int 2x \cos(x^2 - 5) \, dx\), we will use the method of substitution.
Step 1: Let \( u = x^2 - 5 \). Then, \( du = 2x \, dx \). Hence, \( dx = \frac{du}{2x} \).
Step 2: Substitute \( u \) into the integral:
\[ \int 2x \cos(u) \cdot \frac{du}{2x} = \int \cos(u) \, du. \]
Step 3: The integral of \( \cos(u) \) is \( \sin(u) + C \).
Step 4: Substitute back \( u = x^2 - 5 \):
\[ \sin(x^2 - 5) + C. \]
Therefore, the value of the integral is \( \sin(x^2 - 5) + C \).
Step 1: Let \( u = x^2 - 5 \). Then, \( du = 2x \, dx \). Hence, \( dx = \frac{du}{2x} \).
Step 2: Substitute \( u \) into the integral:
\[ \int 2x \cos(u) \cdot \frac{du}{2x} = \int \cos(u) \, du. \]
Step 3: The integral of \( \cos(u) \) is \( \sin(u) + C \).
Step 4: Substitute back \( u = x^2 - 5 \):
\[ \sin(x^2 - 5) + C. \]
Therefore, the value of the integral is \( \sin(x^2 - 5) + C \).
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