Brief Calculus
posted by Ashley .
Decide on what substitution to use, and then evaluate the given integral using a substitution. HINT [See Example 1.] (Round your decimal coefficients to four decimal places.)
x/(2x^2 − 1)^0.4 dx

Brief Calculus 
drwls
Let u = 2x^2 1
Then du = 4x dx, and x*dx = du/4,
x/(2x^2 − 1)^0.4 dx = (du/4)*u^0.4
You can easily integrate that. 
Brief Calculus 
Anonymous
2*x^2=t
2*2xdx=dt
4xdx=dt Divide with 4
xdx=dt/4
Integral of x/(2x^2−1)^0.4 dx=
Integral of dt/4(t1)^0.4=
(1/4) Integral of (t1)^(0.4)dt
Integral of x^n=x^(n+1)/(n+1)
Integral of (t1)^(0.4)dt=
(t1)^(0.4+1)/(0.4+1)+C=
(t1)^0.6/0.6+C=(t1)^(3/5)/0.6+C
Integral of x/(2x^2−1)^0.4 dx=
(1/4) Integral of (t1)^(0.4)dt=
(1/4)(t1)^(3/5)/0.6+C=
(1/4*0.6)(t1)^(3/5)=
(1/2.4)(t1)^(3/5)+C=
0.41666666(t1)^(3/5)+C
t=2x^2
0.41666666(t1)^(3/5)+C=
0.4167(2x^21)^(3/5)+C rounded to 4 decimal pieces
Integral of x/(2x^2−1)^0.4 dx=
0.4167(2x^21)^(3/5)+C 
Brief Calculus 
Ashley
Thanks Guys!
Respond to this Question
Similar Questions

Calculus
Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places. int_2^10 2 sqrt(x^2+5)dx text(, ) n=4 
Calculus
Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places. int_2^10 2 sqrt(x^2+5)dx text(, ) n=4 
calculus
Decide on what substitution to use, and then evaluate the given integral using a substitution. HINT [See Example 1.] (Round your decimal coefficients to four decimal places.) x/(2x^21)^0.4 dx 
Brief Calculus
Evaluate the integral. HINT [See Example 2 and 4.] (Remember to use ln u where appropriate.) (1/v7 + 5/v) dv 
calculus
Calculate the left Riemann sum for the given function over the given interval, using the given value of n. (When rounding, round answers to four decimal places.) f(x) = e^−x over [−6, 6], n = 6 
Math
First, give the technology formula for the given function and then use technology to evaluate the function for the given values of x. (Round your answers to four decimal places.) r(x) = 4x2 + 1/4x2 − 1; x = −1, 0, 1, ..., … 
calculus help
use the midpoint rule with the given value of n to approximate the integral. round the answer to four decimal places. integral 0 to pi/2 2cos^3(x)dx, n=4 M4=? 
Calculus Help Please Urgent!!!
Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places. integral from o to pi/2 (2cos^3(x))dx , n = 4 M4 = ? 
Math
(i) Evaluate integral [ x^3 / (x^2 + 4)^2 ] using trigonometric substitution. (ii) Evaluate integral [ x^3 / (x^2 + 4)^2 ] using regular substitution. (iii) Use a right triangle to check that indeed both answers you obtained in parts … 
Question on Integration
(i) Evaluate integral [ x^3 / (x^2 + 4)^2 ] using trigonometric substitution. (ii) Evaluate integral [ x^3 / (x^2 + 4)^2 ] using regular substitution. (iii) Use a right triangle to check that indeed both answers you obtained in parts …