Integration Help: dx/(5-4x-(x^2))^(5/2)

  • Thread starter Thread starter joseph9496
  • Start date Start date
  • Tags Tags
    Integration
joseph9496
Messages
5
Reaction score
0

Homework Statement



Hi everyone
im stuck with the following integration..

Homework Equations



integral of dx/(5-4x-(x^2))^(5/2)

The Attempt at a Solution



can anyone help me?
thanks
 
Physics news on Phys.org
… complete the square … !

Hi joseph! :smile:

With quadratics, it's usually best to start by completing the square:

5 - 4x - x^2 = 9 - (x + 2)^2.

(And then you can even change to y = x + 2, dy = dx, if you like!)

Does that help? :smile:
 
OH YEAH!
i never thought of that!
thanks alot!
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Verify Green's Theorem in the given problem
Replies
10
Views
2K
Find the result of definite integration
Replies
6
Views
1K
Solve the given second order differential equation
Replies
14
Views
1K
Finding volume using integration
Replies
1
Views
2K
Solve the given problem involving integration
Replies
6
Views
2K
Volume between a region (above x-axis and below parabola) and a surface
Replies
4
Views
2K
Obtain a nonzero solution of ##y''-4y'+x^2(y'-4y)=0## by inspection
Replies
7
Views
2K
Integral using substitution x = -u
Replies
12
Views
2K
Solve ##\int\frac{e^{-x}}{x^2}dx## and ##\int \frac{e^{-x}}{x}dx##
Replies
7
Views
2K
Find the PDF in terms of another variable
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top