Question

Use a change of variables to evaluate the following indefinite integral. \[ \int \frac{(\sqrt{x}+1)^{9}}{2 \sqrt{x}} d x \] Determine a change of variables from \( \mathrm{x} \) to \( \mathrm{u} \). Choose the correct answer below. A. \( u=\frac{1}{2 \sqrt{x}} \) B. \( u=\sqrt{x} \) C. \( u=\sqrt{x}+1 \) D. \( u=(\sqrt{x}+1)^{9} \) Write the integral in terms of \( u \). \[ \int \frac{(\sqrt{x}+1)^{9}}{2 \sqrt{x}} d x=\int(\square) d u \] Evaluate the integral. \[ \int \frac{(\sqrt{x}+1)^{9}}{2 \sqrt{x}} d x= \] \( \square \)

          Use a change of variables to evaluate the following indefinite integral.
\[
\int \frac{(\sqrt{x}+1)^{9}}{2 \sqrt{x}} d x
\]

Determine a change of variables from \( \mathrm{x} \) to \( \mathrm{u} \). Choose the correct answer below.
A. \( u=\frac{1}{2 \sqrt{x}} \)
B. \( u=\sqrt{x} \)
C. \( u=\sqrt{x}+1 \)
D. \( u=(\sqrt{x}+1)^{9} \)

Write the integral in terms of \( u \).
\[
\int \frac{(\sqrt{x}+1)^{9}}{2 \sqrt{x}} d x=\int(\square) d u
\]

Evaluate the integral.
\[
\int \frac{(\sqrt{x}+1)^{9}}{2 \sqrt{x}} d x=
\]
\( \square \)

Show more…

Use a change of variables to evaluate the following indefinite integral.

∫((√(x)+1)^9)/(2 √(x)) d x

Determine a change of variables from x to u. Choose the correct answer below.
A. u=(1)/(2 √(x))
B. u=√(x)
C. u=√(x)+1
D. u=(√(x)+1)^9

Write the integral in terms of u.

∫((√(x)+1)^9)/(2 √(x)) d x=∫(□) d u

Evaluate the integral.

∫((√(x)+1)^9)/(2 √(x)) d x=

□

Added by Victor N.

Calculus Early Transcendentals

Howard Anton, Irl Bivens, Stephen Davis 9th Edition

Chapter 5

Instant Answer

Solved by Expert Ivan Kochetkov

Step 1

The expression \((\sqrt{x}+1)^{9}\) suggests that a good substitution would involve \(\sqrt{x}+1\), because it appears as a composite function. Therefore, the correct choice for \(u\) is: \[ u = \sqrt{x} + 1 \] So, the correct answer is C. \( u=\sqrt{x}+1 \). Show more…

Show all steps

lock

Thanks for your feedback!

Use a change of variables to evaluate the following indefinite integral. \[ \int \frac{(\sqrt{x}+1)^{9}}{2 \sqrt{x}} d x \] Determine a change of variables from \( \mathrm{x} \) to \( \mathrm{u} \). Choose the correct answer below. A. \( u=\frac{1}{2 \sqrt{x}} \) B. \( u=\sqrt{x} \) C. \( u=\sqrt{x}+1 \) D. \( u=(\sqrt{x}+1)^{9} \) Write the integral in terms of \( u \). \[ \int \frac{(\sqrt{x}+1)^{9}}{2 \sqrt{x}} d x=\int(\square) d u \] Evaluate the integral. \[ \int \frac{(\sqrt{x}+1)^{9}}{2 \sqrt{x}} d x= \] \( \square \)

Play audio

Feedback

Powered by NumerAI

Ivan Kochetkov and 91 other subject Calculus 1 / AB 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

Recommended Videos

Recommended Textbooks

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later