In Exercises $29-32,$ guess an antiderivative for the integrand function. Validate your guess by differentiation and then evaluate the given definite integral. (Hint: Keep in mind the Chain Rule in guessing an antiderivative. You will learn how to find such antiderivatives in the next section.) $$\int_{2}^{5} \frac{x d x}{\sqrt{1+x^{2}}}$$
Added by Laurie P.
Step 1
$$\frac{x}{\sqrt{1+x^{2}}}\,dx = \frac{x}{\sqrt{1+x^{2}}}\,dx - x^{2}$$ Show more…
Show all steps
Close
Your feedback will help us improve your experience
Madhur L and 96 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
In Exercises $29-32,$ guess an antiderivative for the integrand function. Validate your guess by differentiation and then evaluate the given definite integral. (Hint: Keep in mind the Chain Rule in guessing an antiderivative. You will learn how to find such antiderivatives in the next section.) $$\int_{0}^{\sqrt{\pi / 2}} x \cos x^{2} d x$$
Integrals
The Fundamental Theorem of Calculus
In Exercises $29-32,$ guess an antiderivative for the integrand function. Validate your guess by differentiation and then evaluate the given definite integral. (Hint: Keep in mind the Chain Rule in guessing an antiderivative. You will learn how to find such antiderivatives in the next section.) $$\int_{0}^{\pi / 3} \sin ^{2} x \cos x d x$$
In Exercises $29-32,$ find the indefinite integral by making a change of variables (Hint: Let $u$ be the denominator of the integrand.) $$\int \frac{4}{1+\sqrt{5 x}} d x$$
Logarithmic, Exponential, and Other Transcendental Functions
The Natural Logarithmic Function: Integration
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD