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 solve the integral \( \int 2x \cos(x^2 - 5) \, dx \), we can use the substitution method.
Step 1: Let \( u = x^2 - 5 \). Then, the differential \( du = 2x \, dx \).
Step 2: Rewrite the integral in terms of \( u \):
\[ \int 2x \cos(u) \, dx = \int \cos(u) \, du. \]
Step 3: Integrate \( \cos(u) \):
\[ \int \cos(u) \, du = \sin(u) + C. \]
Step 4: Substitute back \( u = x^2 - 5 \):
\[ \sin(u) + C = \sin(x^2 - 5) + C. \]
Therefore, the value of the integral is \( \sin(x^2 - 5) + C \). This matches the options presented.
Step 1: Let \( u = x^2 - 5 \). Then, the differential \( du = 2x \, dx \).
Step 2: Rewrite the integral in terms of \( u \):
\[ \int 2x \cos(u) \, dx = \int \cos(u) \, du. \]
Step 3: Integrate \( \cos(u) \):
\[ \int \cos(u) \, du = \sin(u) + C. \]
Step 4: Substitute back \( u = x^2 - 5 \):
\[ \sin(u) + C = \sin(x^2 - 5) + C. \]
Therefore, the value of the integral is \( \sin(x^2 - 5) + C \). This matches the options presented.
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