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Mathematical Expression Editor

Various exercises relating to integration by parts.

Compute the indefinite integrals below. Since there are many possible answers (which
differ by constant values), use the given instructions if needed to choose which
possible answer to use.

(Add a constant to your answer if needed so that it equals at .)

(Add a constant to your answer if needed so that it equals at .)

(Write your answer so that it has no constant term.)

Don’t forget absolute values in your logarithm. (Add a constant to your answer as
necessary so that it equals at .)

(Add a constant to your answer if needed so that it equals at .)

This is a case in
which you need to treat the integration by parts as an equation and solve for the
answer.

(Add a constant to your answer if needed so that it equals at .)

Write
.

Sample Quiz Questions

Compute the definite integral (Hints won’t be revealed until after you choose a
response.)

Integrate by parts, integrating the exponential and differentiating polynomials.

Compute the definite integral (Hints won’t be revealed until after you choose a
response.)

Integrate by parts, integrating the trig functions and differentiating polynomials.

Compute the indefinite integral (Hints won’t be revealed until after you choose a
response.)

Integrate by parts, integrating the coefficient 1 and differentiating arctangent.

Compute the indefinite integral (Hints won’t be revealed until after you choose a
response.)

Integrate by parts, integrating the exponential and differentiating cosine (or
vice-versa), then solve for the antiderivative.

Sample Exam Questions

Compute the integral below.

the integral diverges

Compute the indefinite integral indicated below. [Hint: Write and integrate by
parts.]