Question

Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) 41 / (x^3 − 27) dx , using fraction decomposition.

Answer #1

Evaluate the integral. (Remember to use absolute values where
appropriate. Use C for the constant of integration.)
x2 + 1
(x − 8)(x − 7)2
dx

Make a substitution to express the integrand as a rational
function and then evaluate the integral. (Remember to use absolute
values where appropriate. Use C for the constant of
integration.)
ex
(ex − 3)(e2x + 1)
dx

Evaluate the integral using integration by parts with the
indicated choices of u and dv. (Use C
for the constant of integration.)
xe5xdx; u
= x, dv =
e5xdx
2. Evaluate the integral. (Use C for the constant of
integration.)
(x2 + 10x) cos(x) dx
3. Evaluate the integral. (Use C for the constant of
integration.)
cos−1(x) dx
4. Evaluate the integral. (Use C for the constant of
integration.)
ln(
x
) dx

Evaluate the integral using the indicated trigonometric
substitution. (Use C for the constant of integration.)
x3
x2 + 16
dx
, x = 4
tan(θ)

Find the indefinite integral. (Use C for the constant
of integration.)
x ln(3x) dx

Rewrite the following integral using the indicated order of
integration and then evaluate the resulting integral. Integral from
0 to 3 Integral from negative 1 to 0 Integral from 0 to 4 x plus 4
dy dx dz in the order of dz dx dy

1. Find the partial fraction decomposition of the rational
function:
(2s − 4)/(s^2 + s)(s^2 + 1)
2. Find:
∫ (9x)/(sqrt. root(25-x^2)) dx + ∫ (3)/(sqrt.
root(25-x^2)) dx (use C for constant of integration).
3. Evaluate the following integral:
∫ 17t sin^2(t) dt

Use integration by parts to evaluate the integral:
∫9xcos(−2x)dx

Use Green’s theorem to evaluate the integral: ∫(-x^2y)dx
+(xy^2)dy where C is the boundary of the region enclosed by y=
sqrt(9 − x^2) and the x-axis, traversed in the counterclockwise
direction.

Evaluate the given integral by making an appropriate change of
variables, where R is the trapezoidal region with vertices (3, 0),
(4, 0), (0, 4), and (0, 3).
L = double integral(7cos(7(x-y)/(x+y))dA

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