Need help with d, e, f, and g **Integration Problems**4. Use the appropriate method of integration (rules, substitution, parts, or partial fractions) to evaluate the integral.a. $ \int (x^2 + 6x^2) \, dx $b. $ \int e^{3x} \sec^2 x \, dx $c. $ \int \frac{2x + 6}{x^2 - 3x} \, dx $d. $ \int x^3 \cos x \, dx $e. $ \int x \ln x \, dx $f. $ \int \cos 4x \sin x \, dx $g. $ \int \frac{x^2}{x^3 - 5} \, dx $**Notes and Solutions:**- The calculus problems involve finding the antiderivatives of various functions, applying techniques like substitution or integration by parts where necessary.- The handwritten notes next to some of the problems show attempts at finding the integrals, with standard integration notation and constants of integration $ + C $ indicated.- Some expressions may involve trigonometric or logarithmic functions, along with polynomial expressions that may require algebraic manipulation before integration.**For Further Understanding:**- Review techniques such as integration by substitution, integration by parts, and handling integrals involving trigonometric identities.- Practice similar problems to build fluency in selecting and applying the right method for different types of integrals.

According to bartleby guidelines, for more than three subpart, first three sub part need to be…

al. a. Sx-2 + 6x² dx Jer b. Setanx sec²x dx C. S 2x+ 6 dx x2-3x d. Sx³cosxdx 4 3 \e. fx*lnx dx е. f. S cos*x sin x dx COS X g. S dx x3-5

al. a. Sx-2 + 6x² dx Jer b. Setanx sec²x dx C. S 2x+ 6 dx x2-3x d. Sx³cosxdx 4 3 \e. fxlnx dx е. f. S cosx sin x dx COS X g. S dx x3-5

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Need help with d, e, f, and g

**Integration Problems**

4. Use the appropriate method of integration (rules, substitution, parts, or partial fractions) to evaluate the integral.

a. $ \int (x^2 + 6x^2) \, dx $

b. $ \int e^{3x} \sec^2 x \, dx $

c. $ \int \frac{2x + 6}{x^2 - 3x} \, dx $

d. $ \int x^3 \cos x \, dx $

e. $ \int x \ln x \, dx $

f. $ \int \cos 4x \sin x \, dx $

g. $ \int \frac{x^2}{x^3 - 5} \, dx $

**Notes and Solutions:**

- The calculus problems involve finding the antiderivatives of various functions, applying techniques like substitution or integration by parts where necessary.

- The handwritten notes next to some of the problems show attempts at finding the integrals, with standard integration notation and constants of integration $ + C $ indicated.

- Some expressions may involve trigonometric or logarithmic functions, along with polynomial expressions that may require algebraic manipulation before integration.

**For Further Understanding:**

- Review techniques such as integration by substitution, integration by parts, and handling integrals involving trigonometric identities.

- Practice similar problems to build fluency in selecting and applying the right method for different types of integrals.

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