Question
Evaluate the indefinite integral, using a trigonometric substitution and a triangle to express the answer in terms of $x$$$\int \frac{x^{2}}{\left(1+9 x^{2}\right)^{3 / 2}} d x$$
Step 1
We let $x = \frac{1}{3}\tan(u)$, so $dx = \frac{1}{3}\sec^2(u)du$. Show more…
Show all steps
Your feedback will help us improve your experience
Priyanka Sadarangani and 93 other Calculus 2 / BC educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Evaluate the indefinite integral, using a trigonometric substitution and a triangle to express the answer in terms of $x$ $$\int \frac{x^{2}}{\sqrt{9-x^{2}}} d x$$
Integration
Algebraic Identities and Trigonometric Substitutions
Evaluate the indefinite integral, using a trigonometric substitution and a triangle to express the answer in terms of $x$ $$\int \frac{1}{x \sqrt{9-4 x^{2}}} d x$$
Evaluate the given integral by making a trigonometric substitution (even if you spot another way to evaluate the integral). $$ \int\left(1-9 x^{2}\right)^{3 / 2} d x $$
Techniques of Integration
Trigonometric Substitution
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD