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# Evaluate the indefinite integral of x3e-x2

Compute the following indefinite integral, First, we rearrange the integrand a bit to get a form in which we can make a -substitution, Then, let Therefore, making a -substitution, we have # Evaluate the indefinite integral of ex1/2

Compute the following indefinite integral To evaluate this integral we want to make a substitution. First multiply the numerator and denominator by to obtain, Now define the function by This implies Therefore, using the method of substitution, we have # Evaluate the indefinite integral of x2e-2x

Compute the following indefinite integral, To compute this integral we will integrate by parts twice. First, let Therefore we have To evaluate this next integral we use integration by parts a second time with Giving us So, putting this back into our formula we have # Evaluate the indefinite integral of x2ex

Compute the following indefinite integral, We compute the integral using integration by parts. Let, Then we have But we know from a previous exercise (Section 6.17, Exercise #13) that Therefore we have, # Evaluate the indefinite integral of xe-x

Compute the following indefinite integral, To evaluate this integral we use integration by parts, letting Therefore, # Evaluate the indefinite integral of xex

Compute the following indefinite integral: To evaluate this integral we use integration by parts, letting Then we have, # Find the derivative of eeex

Find the derivative of the following function: Using the chain rule and the formula for the derivative of an exponential we compute, From the previous exercise (Section 6.17, Exercise #11) (or by applying the chain rule and the formula for the derivative of the exponential again) we know Therefore, # Find the derivative of e(ex)

Find the derivative of the following function: Again, we use the chain rule and the formula for the derivative of the exponential, # Find the derivative of elog x

Find the derivative of the following function: Since the derivative is given by We could check this if we wanted by using the chain rule and the derivative of the exponential on the original formula for , # Find the derivative of ecos2x

Find the derivative of the following function: Using the chain rule and the formula for the derivative of the exponential we have, 