NAME THE KEYWORD OR THE METHOD. Keywords: Life-Saving Principle I and the natural log function.

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Presentation transcript:

NAME THE KEYWORD OR THE METHOD

Keywords: Life-Saving Principle I and the natural log function

Keywords: Inverse tangent function

Keywords: Trig substitution leading into the natural log function, or just use the standard formula.

Keywords: Trig substitution leading into the natural log function, or just use the standard formula.

Keywords: Inverse sine function

Keywords: u-substitution. The trig substitution is not necessary, but still will work.

Keywords: Long Division and inverse tangent

Keywords: Trig substitution Now use Integration by Parts and continue

Keywords: Trig substitution Now use Integration by Parts on the remaining integral

Keywords: Partial Fractions! This is because the denominator breaks into factors.

Keywords: Long division followed by Life- Saving Principle I. Partial Fractions is really not be needed.

Keywords: Completing the square, and the inverse tangent.

Keywords: Life-Saving Principle I, leading to the natural logarithm. Partial Fractions are not needed!

Keywords: Partial Fractions

Keywords: Break the integral. Then use Life-Saving Principle I and inverse tangent

Keywords: Break the integral. Then use u-substitution (or candidate method) and a trig substitution (or the standard formula with natural log function)

Keywords: Use a u-substitution or the candidate function method.

Keywords: Use the trig substitution. There is no radical term, but still this substitution really works! Now continue using one of the Double Angle formulas for the cosine

Keywords: Use the trig substitution

Keywords: Use a u-substitution or the candidate function method. The trig substitution is not necessary.

Keywords: Use the trig substitution Now use Integration by parts and continue

Keywords: Use the trig substitution Now use Integration by parts and continue

Keywords: Use Partial Fractions. Since the denominator breaks into factors, this method is better than attempting to complete the square.

Keywords: Life-Saving Principle I, leading to the natural logarithm function. Partial Fractions are not needed, even if the denominator breaks into factors!

Keywords: Partial Fractions are needed!

IT IS CRUCIALTO MEMORIZE THE FOLLOWING FIVE FORMULAS....

MEMORIZE!

LIFE-SAVING PRINCIPLE I