Integration Review Answers and Hints
As the title suggests, what follows are the answers to the integration
practice problems on the Integration Review
page.
Where convenient, hints
are given as to what procedure was used to obtain the answer. See the
Review of Integration Techniques page
for
a short integration table and help with the different techniques of integration.
![](img1.gif)
Use
the substitution u(x)=x^2.
![](img2.gif)
Use integration
by parts with u(x)=theta and v'(x)=cos(theta).
![](img3.gif)
Use integration
by parts twice.
![](img4.gif)
Substitute
u(x) for the function underneath the radical.
![](img5.gif)
Use integration
by parts with u(t)=log(t) and v'(t)=1.
![](img6.gif)
Use the
substitution u(x)=cos(x).
![](img7.gif)
Use
the
identity
![](img14.gif)
![](img8.gif)
Use the
substitution u(x)=cos(x).
![](img9.gif)
Simplify
algebraically and then integrate.
![](img10.gif)
See the
table of integrals.
![](img11.gif)
Use the
method of partial
fractions. The partial fraction decomposition
is
![](img15.gif)
![](img12.gif)
Substitute
u(x) for the function underneath the radical.
![](img13.gif)
Use the
method of partial
fractions. The partial fraction decomposition
is
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