Evaluate Integral INT sqrt(x^2+6x) dx | Get Help Now

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SUMMARY

The integral INT sqrt(x^2+6x) dx can be evaluated using trigonometric substitution after completing the square. The expression simplifies to (x + 3)^2 - 3^2, allowing for a substitution where the hypotenuse is x + 3 and one side is 3. This method streamlines the evaluation process and provides a clear path to the solution.

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  • Understanding of integral calculus
  • Familiarity with trigonometric substitution techniques
  • Knowledge of completing the square in quadratic expressions
  • Basic trigonometric identities and triangle properties
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  • Study trigonometric substitution methods in integral calculus
  • Practice completing the square with various quadratic equations
  • Explore the use of triangles in solving integrals
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Students studying calculus, particularly those focusing on integration techniques, and educators looking for effective methods to teach integral evaluation.

Mr. Goosemahn
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Homework Statement



Evaluate the integral INT sqrt(x^2+6x) dx

The Attempt at a Solution



I honestly have no clue how to even start. I know it involves trigonometric substitution, but I just can't solve it.

Please Help?
 
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Complete the square.
x^2 + 6x + 9 - 9 = (x + 3)^2 - 3^2.

Now you're set to do a trig substitution. I always draw a triangle, since I don't want to clutter up my brain with what formula goes with what substitution. In that case, the hypotenuse should be x + 3, and either the opposite or adjacent side should be 3.
 

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