# Calculus

Evaluate integral(5x-5/3x^2-8x-3) dx.

1. 👍 0
2. 👎 0
3. 👁 186
1. Use partial fractions

(5x-5)/(3x^2 - 8x - 3)
= (5x-5)/((x-3)(3x+1))

let (5x-5)/((x-3)(3x+1))
= A/(x-3) + B/(x-3)
= (A(x-3) + B(3x+1))/((x-3)(3x+1))

so

5x - 5 = A(x-3) + B(3x+1)
let x=3 ----> 10 = B(10) ---> B=1
let x = -1/3
-20/3 = A(-10/3) ----> A = 2

so

(5x-5)/((3x^2 - 8x - 3)
= 2/(x-3) + 1/(3x+1)

and the integral of that is
2ln(x-3) + (1/3)ln(3x+1) + c

1. 👍 0
2. 👎 0
posted by Reiny

## Similar Questions

1. ### calculus

a) Let f(z) = z^2 and γ(t) = 1 + it^3, t ∈ [0,1]. i) Write out the contour integral ∫γ f(z)dz as an integral with respect to t. You do not need to evaluate this integral. ii) Evaluate the integral ∫0,1+i z^2dz iii) What is

asked by jack on March 5, 2016
2. ### Calculus

1. Express the given integral as the limit of a Riemann sum but do not evaluate: integral[0 to 3]((x^3 - 6x)dx) 2.Use the Fundamental Theorem to evaluate integral[0 to 3]((x^3 - 6x)dx).(Your answer must include the

asked by Ernie on May 7, 2018
3. ### Calculus

Evaluate the integral: 16csc(x) dx from pi/2 to pi (and determine if it is convergent or divergent). I know how to find the indefinite integral of csc(x) dx, but I do not know how to evaluate the improper integral.

asked by Sam on June 4, 2012
4. ### calc 3

1. Evaluate the given integral by making an appropriate change of variables, where R is the region in the first quadrant bounded by the ellipse 36x^2+25y^2=1. L= double integral R (4sin(144x^2+100y^2) dA. 2. Use the given

asked by lala on November 4, 2014
5. ### Calculus II/III

A. Find the integral of the following function. Integral of (x√(x+1)) dx. B. Set up and evaluate the integral of (2√x) for the area of the surface generated by revolving the curve about the x-axis from 4 to 9. For part B of

asked by Ryoma on February 19, 2007
6. ### Math (Definite Integrals)

Sketch the region given by the definite integral. Use geometric shapes and formulas to evaluate the integral (a > 0, r > 0). r ∫ sqrt(r^2 - x^2) dx -r While I recognize that this looks similar to a circle function, I'm not sure

asked by Ray on April 6, 2017
7. ### Math

Evaluate the integral of (sin 2x)/(1+cos^2 x) 1. u=cosx and du=-sinx *dx 2. evaluate the integral of -1/(1+u^2)*du 3. result is -ln(1+u^2)+C Where did the sin2x dissapear too???

asked by Dave on September 13, 2017
8. ### Math

Let A denote the portion of the curve y = sqrt(x) that is between the lines x = 1 and x = 4. 1) Set up, don't evaluate, 2 integrals, one in the variable x and one in the variable y, for the length of A. My Work: for x:

asked by Daisy on January 25, 2017
9. ### Calculus

Evaluate the integral: 16csc(x) dx from pi/2 to pi (and determine if it is convergent or divergent). I know how to find the indefinite integral of csc(x) dx, but I do not know how to evaluate the improper integral, at the

asked by Sam on June 5, 2012
10. ### calculus

consider the function f(x) = e^x(sinNx) on the interval [0,1] where N is a positive integer. a) Compute the integral from 0 to 1 of f(x). Evaluate this integral when N=5, N=10, and N=100. B) What happens to the graph and to the

asked by anonymous on February 23, 2010
11. ### calculus

consider the function f(x) = e^x(sinNx) on the interval [0,1] where N is a positive integer. a) Compute the integral from 0 to 1 of f(x). Evaluate this integral when N=5, N=10, and N=100. B) What happens to the graph and to the

asked by Lindsay on February 23, 2010

More Similar Questions