Which of the integrals that follow would be good candidates for trigonometric substitution? If a trigonometric substitution is a good strategy, name the substitution. If another method is a better strategy, explain that method.

(a)4+x2xdx (b)x4+x2dx

role="math" localid="1648759296940" (c)x24+x2dx (d)16x44+x2dx

Short Answer

Expert verified

Ans: (c)x24+x2dx, This expression is good for trigonometric substitution.

Step by step solution

01

Step 1. Given information.

given expressions,

(a)4+x2xdx (b)x4+x2dx

(c)x24+x2dx (d)16x44+x2dx

02

Step 2. (a)  The expression is as follows,

4+x2xdx

The above integral can be solved using algebra.

03

Step 3. (b)  The expression is as follows, 

x4+x2dx

The above integral can be solved using the conventional substitution with u=4+x2,du=2xdx.

04

Step 4.  (c)  The expression is as follows, 

x24+x2dx

The above integral can be solved using the trigonometric substitution with x=2tanu

05

Step 4.  (d)   The expression is as follows,  

16x44+x2dx

The above integral can be solved using algebra after writing16x4=4x24+x2

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