When evaluating the integral $\int t^3 (t^4 - 7)^{24} dt$, the best substitution is and the solution is When identifying the substitution, be sure to include the standard variable such a u, dv, du, or $\theta$ and format the substitution as an equation like $x = \tan(\theta)$ or $u = e^{4x}$
Added by Antonio W.
Close
Step 1
Step 1: The integral is ∫24dt. Show more…
Show all steps
Your feedback will help us improve your experience
Zhumagali Shomanov and 65 other Calculus 1 / AB 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
Find an appropriate choice of u and dv for integration by parts of each integral. Do not evaluate the integral. ∫x ln x dx; u =?, dv=?
Zhumagali S.
Indicate a good method for evaluating the integral (but do not evaluate). Your choices are: substitution (specify $u$ and $d u $) Integration by Parts (specify $u$ and $d v $), a trigonometric method, or trigonometric substitution (specify). If appears that these techniques are not sufficient, state this. $\int \frac{d x}{(x+12)^{4}}$
TECHNIQUES OF INTEGRATION
Strategies for Integration
Decide on what substitution to use, and then evaluate the given integral using a substitution. HINT [See Example 1.] $$ \int \frac{2 e^{2 / x}}{x^{2}} d x $$
The Integral
Substitution
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD