Given the integral { \int (x^3-(4-x^2))dx } , which of the following substitutions would best...

Question:

Given the integral

{eq}\int (x^3-(4-x^2))dx {/eq} , which of the following substitutions would best solve the integral:

{eq}a. x = \sqrt{sin(u)}\\b. x = 2tant\\c. x = 2sint\\d. x = 2sect\\e. x = u^2 {/eq}

Indefinite integral

The best way to calculate this integral is without any substitution, because the integrand is a polynomial function. On the other hand, if you have to use one of the given preposition for a substitute, you should use an appropriate sine function from reasons explaind below.

Answer and Explanation:

The answer is c, since {eq}4-4\sin^2 t = 4\cos^2 t {/eq}.


Learn more about this topic:

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Indefinite Integral: Definition, Rules & Examples

from Calculus: Tutoring Solution

Chapter 7 / Lesson 14
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