Question

integration of u^2 sinha(t-u) du

Answer 1

\[ \int u^2 \sinh a(t-u) \; du\]

Answer 2

how will i derive

Answer 3

try integration by parts

Answer 4

Woops!! this doesn't have closed form in elementry functions
http://www.wolframalpha.com/input/?i=integrate+u^2+sinh%28a%28t-u%29%29+du

Answer 5

but it doesn't show the steps

Answer 6

and i am little weak in it

Answer 7

hold on ... i'll check again.

Answer 8

sure

Answer 9

http://www.wolframalpha.com/input/?i=integrate+sinh%28a%28t-u%29%29+du

Answer 10

you sure that 'a' is there?

Answer 11

yes

Answer 12

the problem is from the book of laplace transformation by spiegel

Answer 13

Use Integration by parts
\[\int u^2 \sinh (a(t-u)) du\]
\[u^2\cosh (a(t-u))-\int \frac{d}{du} u^2 \times \int (\sinh (a(t-u))\]
\[u^2\cosh (a(t-u))/(-a)-\int 2x \times \sinh (a(t-u))/(-a)\]
Now apply by parts on second term