calculate-x-2-1-sh-3x-dx-

Question Number 76193 by abdomathmax last updated on 25/Dec/19

c a l c u l a t e \int (x^{2} - 1) s h (3 x) d x

Commented by benjo last updated on 25/Dec/19

sir do you mean sh (3 x) = \sinh (3 x) ?

Commented by mathmax by abdo last updated on 25/Dec/19

y e s

Commented by abdomathmax last updated on 25/Dec/19

l e t I = \int (x^{2} - 1) s h (3 x) d x b y p a r t s

I = \frac{x^{2} - 1}{3} c h (3 x) - \frac{1}{3} \int (2 x - 1) c h (3 x) d x

a g a i n b y p a r t s \int (2 x - 1) c h (3 x) d x

= \frac{2 x - 1}{3} s h (3 x) - \frac{2}{3} \int s h (3 x) d x

= \frac{2 x - 1}{3} s h (3 x) - \frac{2}{9} c h (3 x) + c \Rightarrow

I = \frac{x^{2} - 1}{3} c h (3 x) - \frac{2 x - 1}{9} s h (3 x) + \frac{2}{27} c h (3 x) + C

Commented by benjo last updated on 26/Dec/19

sir i think missing in (2 x - 1) / 9

Answered by benjo last updated on 25/Dec/19

= (1 / 3) (x^{2} - 1) \cosh (3 x) - (2 / 9) x

\sinh (3 x) + (2 / 27) \cosh (3 x) + C

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