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find the indefinite integral using the substitution x = 4 sin 0. 5. J(16 – x²}9/2 dx dx 7. V16 – x² xp. 8. 16 – x² xp

find the indefinite integral using the substitution x = 4 sin 0. 5. J(16 – x²}9/2 dx dx 7. V16 – x² xp. 8. 16 – x² xp

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Using Trigonometric Substitution** In Exercises 5–8, find the indefinite integral using the substitution \( x = 4 \sin \theta \). 5. \(\int \frac{1}{(16 - x^2)^{3/2}} \, dx\) 6. \(\int \frac{4}{x^2 \sqrt{16 - x^2}} \, dx\) 7. \(\int \frac{\sqrt{16 - x^2}}{x} \, dx\) 8. \(\int \frac{x^3}{\sqrt{16 - x^2}} \, dx\)
Transcribed Image Text:**Using Trigonometric Substitution** In Exercises 5–8, find the indefinite integral using the substitution \( x = 4 \sin \theta \). 5. \(\int \frac{1}{(16 - x^2)^{3/2}} \, dx\) 6. \(\int \frac{4}{x^2 \sqrt{16 - x^2}} \, dx\) 7. \(\int \frac{\sqrt{16 - x^2}}{x} \, dx\) 8. \(\int \frac{x^3}{\sqrt{16 - x^2}} \, dx\)
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