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Compute
e
^{sin(x)}cos(x)dx
.
Find
tan(x)dx
.
Compute
1/()dx
.
Compute
2sin(x)cos(x)dx
.
Find
dx


Compute
x
^{2}
e
^{x3+7}
dx
.
In order to integrate a function that is a product of an easily integrable function with an
easily differentiable one, it is often useful to employ
The method of integration that is closely related to the chain rule for differentiation is the
Compute
5xe
^{x}
dx
.
Compute
(log(x))^{2}/xdx
.
Find
 4dx
Determine the value of
Π/x
^{2}
dx
.
Find
2
dx
.
Compute the area between the graphs of the functions
f (x) = x
^{2}  4x + 3
and
g(x) =  x
^{2} + 4x  3
.
Find the area between the graphs of
x
^{2}  3
and
2x  3
.
Find the volume of the solid given by revolving the region below the graph of
6  3x
from
0
to
2
about the
y
axis.
Compute the volume of the solid given by revolving the region below the graph of
x
^{2}  4x + 5
from
x = 0
to
2
about the
y
axis.
Compute the volume of the solid given by revolving the region below the graph of
sin(x)
from
0
to
Π
about the
y
axis.
Compute the volume of the solid given by revolving the region below the graph of
sin(x)
from
0
to
Π
about the
x
axis.
Determine the volume of the solid given by revolving the region below the graph of
e
^{2x}
from
x = 1
to
2
about the
x
axis.
Compute the volume of the solid given by revolving the region below the graph of
f (x) = 2
from
x =  2
to
1
about the
x
axis.
Find
sin(x)e
^{x}
dx
.
Compute
x
^{4}log(x)dx
.
Find the value of
cos^{2}(x)(1 + tan^{2}
x)dx
.
Determine the radius of convergence of
5( 1)^{n}
x
^{n}
.
What is the radius of convergence of
(x  1)^{n}/n!
?
Find the integral of
( 1)^{n1}
x
^{n}/n
(on its radius of convergence).
What is the value of
6(1/3)^{n}
?
Compute
dx


Compute
dx


Find
dx


Compute
dx


Compute
1/(x  1)^{2}
.
Find
x/(x  1)^{2}
dx
.
It is possible for a series with positive terms to converge but not
Determine the value of
1/(n log(n))
.
Find
1/(x(log(x))^{2})dx
.
For which values of
k
does the series
4/(n + 1)^{k}
converge?
The Taylor series of a function is a kind of
Find the length of the parametric curve
(3 + 2 sin(t), 1 + 2 cos(t))
from
t = 0
to
Π
.
How many petals are on the "flower" formed by the polar curve
r(θ) = sin(4θ)
?
What is the velocity vector to the parametric curve
(e
^{t} + cos(t), 3t + 2)
at time
t = 2Π
?
Find the acceleration vector for the parametric curve
(sin(t)cos(t), log(t))
at time
t
.
Find the speed of the particle whose motion in the plane is given by
(log(27x
^{2}), 3x)
.
Determine the area below the polar curve
r(θ) = 3θ
^{2} + 2
from
θ = 0
to
1
.
Compute the area below the graph of the polar curve
r(θ) = e
^{
θ
}
from
θ = 2
to
t
.
Find the area between the parametric curves
(t, t
^{2}  1)
and
(t,  t
^{2} + 1)
.
The set of points on a unit circle could not be
To derive the formula for the length of the parametric curve, one may