What is the integral of sin(x)+sinh(x) ?

The integral of sin(x)+sinh(x) is -cos(x)+cosh(x)+C

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integral of sin(x)+sinh(x)

\int sin (x) + sinh (x) d x

- cos (x) + cosh (x) + C

Solution steps

\int sin (x) + sinh (x) d x

Apply the Sum Rule:

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

= \int sin (x) d x + \int sinh (x) d x

\int sin (x) d x = - cos (x)

\int sinh (x) d x = cosh (x)

= - cos (x) + cosh (x)

Add a constant to the solution

= - cos (x) + cosh (x) + C

\frac{d y}{d x} = \frac{( 10 + 15 x )}{x y ^{2}}, y (1) = 3

\frac{\partial}{\partial x} (x \cdot y)

\int \frac{3 x ^{2}}{1 + x ^{3}} d x

\frac{\partial}{\partial x} (16 - x^{2} - 4 y)

x \to \infty lim (\frac{2}{x !})

What is the integral of sin(x)+sinh(x) ?
The integral of sin(x)+sinh(x) is -cos(x)+cosh(x)+C