Question

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

Answer #1

Find the partial fraction decomposition of the rational
function. 9?^2 − 9? + 6 all over 2?^3 − ?^2 − 8? + 4

Use partial fraction decomposition to find the inverse Laplace
transform of the given function.
(a) Y (s) = 2 /(s 2+3s−4)
(b) Y (s) = 1−2s /(s 2+4s+5)
differential eq

integration by partial fraction decomposition from -2 to 2.
(x^3+2)/((x+5)(x+4))dx

Find the partial fraction decomposition of the following
rational expression.
3x3 + 11x2 + 24x + 43
(x + 3)2(x2 + 2)

integral using partial fraction decomposition. ( x^3 + 2x + 5) /
((x + 1)(x 2 + 1))dx

Evaluate the integral using Partial fraction decomposition
(PLEASE SHOW EVERY STEPS: the dummy decomposition form, specific
decomposition form, and the linear system that must be solved to
get from one to the other. Make sure to Label every step and
explain the process
The integral (-t^2+33t+18)/(t^3-9t)dt

1. ∫3xe^4x dx =
2. Use integration by parts to evaluate the integral:
∫2s cos(s)ds

Write out the form of the partial fraction decomposition of the
function appearing in the integral:
∫2x−92x2+4x−5,dx∫2x-92x2+4x-5,dx
Determine the numerical values of the coefficients, A and B, where
A ≤≤ B.
Adenominator+BdenominatorAdenominator+Bdenominator

Write the partial fraction decomposition of the following
rational expression.
(x^2-5x+12)/(x-5)(x-2)(x+1)

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

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