3. Solve the following: 2xdx (x²+1)2 a. b. y = f xe* dx, given y=0 when x=0 x-2x+1 dx с. d. sn (Inx) xlnx e. S(e5x – 8*)dx

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A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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Q: 2. e3x* (y + 6x²y)dxdy =?

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Q: 5. Determine the average value of f(x) over the interval from x = a to x = b, where a) f (x) = x²; a…

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Q: Find ∫ √(3 − 5x) /2x   dx.

A: Consider the given integral, ∫3-5x2xdx substitute 3-5x=u ⇒ dx=-23-5x5 ∫3-5x2xdx=2∫u2u2-3du now,…

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A:

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Q: dr Find if r (x) = 9x 2 + 5x – 3. dx

A: Given,            r(x) = 9x2 + 5x - 3