How do you solve for x, ln ( (x^2) +1)=cos x??

Question

I need to find x for the limits of integration for integral of cosx- ln (x^2 +1) dx, to find the area, volume, and arc length, of the region they bounded. My calculator gives an estimate, as x= + or - .9158576564, but id like an exact value. Thanks alot for the help. Its Greatly apperciated.

"It is a transcendental equation. The answer will be a transcendental number which has an infinite number of digits following the decimal point, like π."

-Yeah, I know that the number is irrational. But I want it to be exact, like 22/7 is a reasonable estimation of pi, but in higher math, just pi is used, no estimations. I want to know the EXACT values of x, whether is pi/ln (pi)/ln .05, watever it may be...

I rewrote the equation many times, and I get stuck also...I think I have to use the quadratic formula, but that e^cos x confuses me...

Answer 1

Well, I am a bit rusty in the algebra dept..

You can rewrite the equation a bit:
ln ( (x^2) +1)=cos x

this is equal to:

x^2 + 1 = e^(cos x)

which results in

x^2 = e^(cos x) - 1

which yields

x = sqrt (e^(cos x) - 1)

beyond that I am stuck without a book or whatever :)

Somehow I think you will not have much use from my answer, sorry

Answer 2

It is a transcendental equation. The answer will be a transcendental number which has an infinite number of digits following the decimal point, like π.

Answer 3

x^2+1=1
x^2=0
x=0

Answer 4

Volume?!!x,y,z?!!,
but in higher math
like how high, like 数字理论