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October 25, 2014

October 25, 2014

Posted by **Amy** on Wednesday, March 23, 2011 at 11:40am.

Evaluate the integrals:

1.) ∫ (2-2cos^2x) dx

2.) ∫ cot3x dx

3.) ∫ ((e^(sqrt x) / (sqrt x) dx))

- Calculus - evaluating integrals -
**Reiny**, Wednesday, March 23, 2011 at 12:21pm1.) ∫ (2-2cos^2x) dx

= ∫ (2-2cos^2x) dx

= ∫ (1-(2cos^2x-1)) dx

= ∫ (1-cos 2x) dx

= x - (1/2)sin 2x + c

2.

∫ cot3x dx

= ∫ cos3x/sin 3x dx

= (1/3) ln(sin 3x) + c

3.

∫ (e^√x / √x dx

= ∫ e^(x^(1/2)) (e^(-1/2)) dx

= 2 e^(x^(1/2)) + c or 2 e^√x + c

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