Question

integrate 1/(x^2) sinh (1/x) dx

Answer 1

u=1/x

Answer 2

smooth

Answer 3

then 1/x^2 will become u^2?

Answer 4

\(\color{#000000 }{ \displaystyle \int\color{red}{\frac{1}{x^2}}\color{blue}{\sinh\left(\frac{1}{x}\right)}\color{red}{dx} }\)

\(\color{#0000ff }{ \displaystyle u=1/x }\)
\(\color{#ff0000 }{ \displaystyle du=-1/x^2{\tiny~}dx\quad \Longrightarrow \quad -du=1/x^2{\tiny~}dx }\)

Answer 5

substitute accordingly...
you are probably just too tired working these out :)

Answer 6

the (1/x²)dx goes away and is replaced by -du.
And 1/x inside sinh is replied by u.

Answer 7

ill do it again,

Answer 8

(I shouldn't have coloered "sinh" in blue) ...\
sure :)

Answer 9

\(\color{#000000 }{ \displaystyle \int f'(x)\cdot {\bf G}\left\{f(x)\right\} dx}\)

\(\color{#000fc0 }{ \displaystyle u=f(x)}\)
\(\color{#000fc0 }{ \displaystyle du=f'(x){\tiny~}dx}\)

\(\color{#000000 }{ \displaystyle \int {\bf G}\left\{u\right\} du}\)

Answer 10

that is typically the setup ... your probably isn't different ... (I've seen you do harder integrals before)

Answer 11

ok, i got it

Answer 12

yayy

Answer 13

Alright; nice to hear that!

Answer 14

thanks