Question

Evaluate the following integral using trigonometric substitution.\ $int frac{dx}{(441 + x^2)^{frac{3}{2}}}$

Name: Evaluate the following integral using trigonometric substitution.int fracdx(441 + x^2)^frac32
Uploaded: 2023-09-03T16:07:21-08:00
Duration: 3 min 15 s
Channel: Adi S
Description: Evaluate the following integral using trigonometric substitution.int fracdx(441 + x^2)^frac32

          Evaluate the following integral using trigonometric substitution.\
$int frac{dx}{(441 + x^2)^{frac{3}{2}}}$

$Evaluate the following integral using trigonometric substitution.int fracdx(441 + x^2)^frac32$

Added by Charles S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/03/2023

Step 1

Then, we have: $$\int \frac{21\sec^2(\theta)d\theta}{\sqrt{441+2(21\tan(\theta))^2}}$$ Simplify the expression inside the square root: $$\sqrt{441+2(21\tan(\theta))^2} = \sqrt{441+882\tan^2(\theta)}$$ Now, use the identity $\tan^2(\theta) + 1 = Show more…

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