- #1

- 8

- 0

How do you integrate

1. 1/(1-x^5)

2. 1/(1+x^4)

and the trig question.

Show that

(a^2 - b^2)/c^2 = sin(A-B)/sin(A+B)

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- Thread starter alamin
- Start date

- #1

- 8

- 0

How do you integrate

1. 1/(1-x^5)

2. 1/(1+x^4)

and the trig question.

Show that

(a^2 - b^2)/c^2 = sin(A-B)/sin(A+B)

- #2

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 964

To factor 1- x

Same for 1/(1+x

In the trig question, are we to assum that a, b, and c are lengths of sides opposite angles A, B, C? In a right triangle or general triangle?

- #3

- 8

- 0

a,b,c are length's

A,B,C are opposite angles

Sorry but i made a mistake in the first integration question

its suppose to be 1/sqrt(1-x^5)

When i used this integration in mathematica 5 : i got something like hypergeometric2f1....

Can u help me out!

- #4

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 964

1, cos(72)+ i sin(72), cos(144)+ i sin(144), cos(216)+ i sin(216), cos(288)+ i sin(288).

Since cos(72)= cos(288), sin(72)= -sin(288), cos(144)= cos(216), and sin(144)= sin(216), these are in pairs of complex conjugates (as they have to be in order to satisfy and equation with real coefficients.

The solutions to x

1- x= -(x-1)(x- cos(72)+ i sin(72))(x- 72- i sin(72))(x- cos(144)+ isin(144))(x- cos(144)- i sin(144))= -(x-1)((x-cos(72))

= -(x-1)(x

Once you have that factorization you can expand 1/(1- x

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