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Integration and Differentiation

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1. Evaluate the integrals.

a. Integral of cot cubed root of x / cubed root of x^2 dx
b. Integral of cos^2x / sinx dx
c. Integral of cosx sinx / cos^2x-1

2. Solve the differential equation subject to the given conditions.

y'' = 6 e^2x ; y = -3 and y' = 2 if x = 0

3. Find f'(x) for each of the following f(x).

a. (e^4x-5)^3
b. sec^2(e^-4x)
c. x e^cotx
d. ln(csce^3x)

4. Use implicit differentiation to find y'.

a. E^xy-x^3+3y^2 = 11
b. E^x cosy = xe^y

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Solution Summary

Solve the differential equation in this case.

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