What is the integral of t^2sinh(t) ?

The integral of t^2sinh(t) is t^2cosh(t)-2(tsinh(t)-cosh(t))+C

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integral of t^2sinh(t)

\int t^{2} sinh (t) d t

t^{2} cosh (t) - 2 (t sinh (t) - cosh (t)) + C

Solution steps

\int t^{2} sinh (t) d t

Apply Integration By Parts

: t^{2} cosh (t) - \int 2 t cosh (t) d t

= t^{2} cosh (t) - \int 2 t cosh (t) d t

\int 2 t cosh (t) d t = 2 (t sinh (t) - cosh (t))

= t^{2} cosh (t) - 2 (t sinh (t) - cosh (t))

Add a constant to the solution

= t^{2} cosh (t) - 2 (t sinh (t) - cosh (t)) + C

\int_{0}^{1} \frac{x ^{2}}{x ^{3} + 1} d x

x \to 0.01 lim (\frac{e ^{x} - 1}{x})

\frac{d}{d x} (\frac{sin ( \frac{1}{x} ) x ^{3}}{ln ( x )})

1 - x^{2}, x^{6} - x + 1

x \to - \infty lim (x^{4} + x)

What is the integral of t^2sinh(t) ?
The integral of t^2sinh(t) is t^2cosh(t)-2(tsinh(t)-cosh(t))+C