Calculus/Indefinite integral/Solutions

1. Evaluate We need to find a function, , such that We know that So we need to find a constant, , such that Solving for , we get So Check your answer by taking the derivative of the function you've found and checking that it matches the integrand: 2. Find the general antiderivative of the function . We know that We need to find a constant, , such that Solving for , we get So the general antiderivative will be Check your answer by taking the derivative of the antiderivative you've found and checking that you get back the function you started with: 3. Evaluate 4. Evaluate 5. Evaluate by making the substitution Since , and 6. Evaluate Let , so that 7. Evaluate using integration by parts with and ; 8. Evaluate Let ; Then and To evaluate , make the substitution ; ; . Then . So