What is the integral from 0 to x of sinh^2(t) ?

The integral from 0 to x of sinh^2(t) is 1/2 (-x+1/2 sinh(2x))

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integral from 0 to x of sinh^2(t)

\int_{0}^{x} sinh^{2} (t) d t

\frac{1}{2} (- x + \frac{1}{2} sinh (2 x))

Solution steps

\int_{0}^{x} sinh^{2} (t) d t

Rewrite using trig identities

= \int_{0}^{x} \frac{- 1 + cosh ( 2 t )}{2} d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{0}^{x} - 1 + cosh (2 t) d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (- \int_{0}^{x} 1 d t + \int_{0}^{x} cosh (2 t) d t)

\int_{0}^{x} 1 d t = x

\int_{0}^{x} cosh (2 t) d t = \frac{1}{2} sinh (2 x)

= \frac{1}{2} (- x + \frac{1}{2} sinh (2 x))

\int_{0}^{t} e^{- a x} d x

\int_{- 2}^{2} x (x^{2} + 1)^{2} d x

\int_{0}^{1} x^{2} cos (x) d x

\int_{\frac{π}{4}}^{π} ∣ cos (x) ∣ d x

\int_{0}^{1} (2 t + 1) e^{- s t} d t

What is the integral from 0 to x of sinh^2(t) ?
The integral from 0 to x of sinh^2(t) is 1/2 (-x+1/2 sinh(2x))