b2sonicxh
2022-01-04
Answered

How do I integrate the following:

$\int \frac{1+{x}^{2}}{(1-{x}^{2})\sqrt{1+{x}^{4}}}dx$

You can still ask an expert for help

Stuart Rountree

Answered 2022-01-05
Author has **29** answers

Let

Then

Now

Thus

Elaine Verrett

Answered 2022-01-06
Author has **41** answers

Somewhat inspired by Morons

karton

Answered 2022-01-11
Author has **368** answers

Without loss of generality we may assume that 1>x>0. Put

Introduce the new variable

Then we have

Substituting back we obtain

Putting back everything we obtain

asked 2022-01-03

Show that

${\int}_{0}^{\mathrm{\infty}}\frac{x\mathrm{cos}ax}{\text{sinh}x}dx\frac{{\pi}^{2}}{4}{\text{sech}}^{2}\left(\frac{a\pi}{2}\right)$

asked 2022-03-19

Can someone simply explain to me how to calculate linear integral linke below?

${\int}_{L}5ydL$

where L is line segment from (0;0) to (0,2;0,2)

where L is line segment from (0;0) to (0,2;0,2)

asked 2022-01-04

Evaluate the integral:

$\int \mathrm{sin}\left({x}^{3}\right)dx$

asked 2020-10-25

Evaluate the integral. ${\int}_{0}^{1}\frac{(x-4)}{({x}^{2}-5x+6dx)}$

asked 2022-01-06

Consider the following integral:

$I={\int}_{0}^{\mathrm{\infty}}\frac{x-1}{\sqrt{{2}^{x}-1}\mathrm{ln}({2}^{x}-1)}dx$

asked 2022-01-25

How is the integral $\frac{2}{\pi}{\int}_{0}^{\pi}{x}^{2}\mathrm{cos}\left(nx\right)dx=\frac{4{(-1)}^{n}}{{n}^{2}}$ ?

I thought it would be this :

$\frac{2}{\pi}{\int}_{0}^{\pi}{x}^{2}\mathrm{cos}\left(nx\right)dx=\frac{2}{\pi}{\int}_{0}^{\pi}{x}^{2}{(-1)}^{n}=\frac{2}{\pi}{(-1)}^{n}{\int}_{0}^{\pi}{x}^{2}=\frac{2}{\pi {(-1)}^{n}}{\left[\frac{{x}^{3}}{3}\right]}_{0}^{\pi}=\frac{2{(-1)}^{n}}{3{\pi}^{3}}$

But it is actually

$\frac{2}{\pi}{\int}_{0}^{\pi}{x}^{2}\mathrm{cos}\left(nx\right)dx=\frac{4{(-1)}^{n}}{{n}^{2}}$

I thought it would be this :

But it is actually

asked 2021-09-01

Find the area of the part of the plane