(a) By explicitly changing the bounds of integration, compute $\int_1^2 x^5 \sqrt{x^3 + 8} dx.$
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Since we are changing the bounds from 1 to 2, we need to find the new limits of integration by substituting x = 1 and x = 2 into the expression x^(5)√(x^(3)+8). Show more…
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Adi S.
(a) Make an appropriate $u$-substitution, and then use the Endpaper Integral Table to evaluate the integral. (b) If you have a CAS, use it to evaluate the integral (no substitution), and then confirm that the result is equivalent to that in part (a). $$\int x \sin 3 x \, d x$$
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(a) Use the Endpaper Integral Table to evaluate the integral. (b) If you have a CAS, use it to evaluate the integral, and then confirm that the result is equivalent to the one that you found in part (a). $$\int \frac{3 x}{4 x-1} d x$$
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