- #1
ardentmed
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This thread is only addressing question 6.
6a and 6b seemed relatively simple, with 6c seeming to be the most troublesome. I got 1/4 arcsin (x^2 / 2 ) + c for 6a after substituting u for x^2.
As for 6b, I got (x^2)/2 -2ln(x^2 +4) + c after using algebraic division and taking u=x^2 + 4.
Finally, for 6c, I took u as √(x), followed by algebraic division since the nominator should always be smaller than the denominator in order for partial fractions to be usable. This gave me 2√(x) + 2ln(√x -2 ) - 2ln(√x + 2) + c.
6a and 6b seemed relatively simple, with 6c seeming to be the most troublesome. I got 1/4 arcsin (x^2 / 2 ) + c for 6a after substituting u for x^2.
As for 6b, I got (x^2)/2 -2ln(x^2 +4) + c after using algebraic division and taking u=x^2 + 4.
Finally, for 6c, I took u as √(x), followed by algebraic division since the nominator should always be smaller than the denominator in order for partial fractions to be usable. This gave me 2√(x) + 2ln(√x -2 ) - 2ln(√x + 2) + c.