What is the integral of 10sin(t)+3cos(t) ?

The integral of 10sin(t)+3cos(t) is -10cos(t)+3sin(t)+C

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integral of 10sin(t)+3cos(t)

\int 10 sin (t) + 3 cos (t) d t

- 10 cos (t) + 3 sin (t) + C

Solution steps

\int 10 sin (t) + 3 cos (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

= \int 10 sin (t) d t + \int 3 cos (t) d t

\int 10 sin (t) d t = - 10 cos (t)

\int 3 cos (t) d t = 3 sin (t)

= - 10 cos (t) + 3 sin (t)

Add a constant to the solution

= - 10 cos (t) + 3 sin (t) + C

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

\frac{d}{d x} (\frac{e ^{x}}{1 + x})

y = 7 cos (x), (\frac{π}{3}, 3.5)

\frac{2}{s ^{2} + 2 s}

\frac{d y}{d t} = \frac{9}{40} - \frac{y}{200}, y (0) = 90

What is the integral of 10sin(t)+3cos(t) ?
The integral of 10sin(t)+3cos(t) is -10cos(t)+3sin(t)+C