Can i do this to make this integral more simple

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In summary, substitution is a commonly used technique to simplify integrals by replacing a variable with a new one. There are various methods for simplifying integrals, including integration by parts, trigonometric substitution, and partial fraction decomposition. Splitting an integral into smaller parts can also make it more manageable. Functions such as polynomials, exponential functions, and trigonometric functions are generally easier to integrate than rational functions or functions involving radicals. To determine if an integral is even or odd, one can check the limits of integration or see if the integrand is unchanged when x is replaced with -x (even) or -x (odd).
  • #1
vande060
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Homework Statement



S cos^5x/sin^1/2x

Homework Equations


The Attempt at a Solution



S cos^5x/sin^1/2x

t = sin^1/2x
t^2 = sinx

2t dt = cosx dx

substituting back in

S 2tcos^4x/t
S 2cos^4x
 
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  • #2
Try substituting just t=sin(x).
 
  • #3
Dick said:
Try substituting just t=sin(x).

i got it thanks
 

1. Can I use substitution to simplify this integral?

Yes, substitution is a commonly used technique to simplify integrals. It involves replacing a variable with a new one in order to make the integral easier to solve.

2. Is there a specific method I can use to make this integral simpler?

Yes, there are various techniques for simplifying integrals, such as integration by parts, trigonometric substitution, and partial fraction decomposition. It is important to choose the most appropriate method based on the form of the integral.

3. Can I split this integral into smaller parts to make it easier?

Yes, sometimes splitting an integral into smaller parts can make it more manageable. This is particularly useful for integrals involving piecewise functions or functions with multiple terms.

4. Is there a certain type of function that is easier to integrate?

Yes, some functions are easier to integrate than others. Generally, polynomials, exponential functions, and trigonometric functions are simpler to integrate compared to rational functions or functions involving radicals.

5. How can I tell if an integral is even or odd?

If the limits of integration for an integral are -a to a, the function being integrated is even. If the limits are -a to a, the function is odd. Alternatively, you can check if the integrand is unchanged when x is replaced with -x (even) or -x (odd).

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