Question

Choosing a Formula In Exercises $5-14$ , select the basic integration formula you can use to find the integral, and identify $u$ and $a$ when appropriate. $$ \int \frac{2}{(2 t-1)^{2}+4} d t $$

Name: Problem 8, Chapter 8: Calculus of a Single Variable
Uploaded: 2019-06-25T02:57:07-08:00
Duration: 1 min 29 s
Channel: Ashley Boni
Description: Choosing a Formula In Exercises 5-14 , select the basic integration formula you can use to find the integral, and identify u and a when appropriate. ∫(2)/((2 t-1)^2+4) d t

   Choosing a Formula In Exercises $5-14$ , select the basic integration formula you can use to find the integral, and identify $u$ and $a$ when appropriate. 
$$
\int \frac{2}{(2 t-1)^{2}+4} d t
$$

Calculus of a Single Variable

Ron Larson, Bruce… 10th Edition

Chapter 8, Problem 8

Instant Answer

Solved by Expert Ashley Boni

06/25/2019

Step 1

Looking at the integrand, we see that it is a rational function of the form $\frac{1}{(u^2 + a^2)}$. This suggests that we can use the formula: $$\int \frac{1}{u^2 + a^2} du = \frac{1}{a} \arctan\left(\frac{u}{a}\right) + C$$ where $u$ and $a$ are appropriate Show more…

Show all steps

Thanks for your feedback!

Choosing a Formula In Exercises $5-14$ , select the basic integration formula you can use to find the integral, and identify $u$ and $a$ when appropriate. $$ \int \frac{2}{(2 t-1)^{2}+4} d t $$

Play audio

Feedback

Ashley Boni and 86 other subject Calculus 2 / BC educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Inverse Tangent Integration Formula

The inverse tangent integration formula, ? du/(u² + a²) = (1/a) arctan(u/a) + C, is a key formula used for integrating functions that match the structure of a sum of a squared variable and a constant. Identifying the appropriate substitution and constant a allows the integrand to be expressed in this standard form, facilitating straightforward application of the formula.

u-Substitution

u-Substitution is a fundamental technique in integration used to simplify an integral by introducing a new variable, often denoted as u, to replace a function of the original variable. This method transforms the integral into a form that is easier to handle by aligning it with a basic integration formula.

Please give Ace some feedback