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Calculus - evaluating integrals

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I'm really having trouble with this current topic that we're learning. Any explanations are greatly appreciated.

Evaluate the integrals:

1.) ∫ (2-2cos^2x) dx

2.) ∫ cot3x dx

3.) ∫ ((e^(sqrt x) / (sqrt x) dx))

  • Calculus - evaluating integrals - ,

    1.) ∫ (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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