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

The integral of sin(3x)+10cos(x) is -1/3 cos(3x)+10sin(x)+C

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

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

- \frac{1}{3} cos (3 x) + 10 sin (x) + C

Solution steps

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

\int sin (3 x) d x = - \frac{1}{3} cos (3 x)

\int 10 cos (x) d x = 10 sin (x)

= - \frac{1}{3} cos (3 x) + 10 sin (x)

Add a constant to the solution

= - \frac{1}{3} cos (3 x) + 10 sin (x) + C

g (x) = x

6 sec (x)

\frac{d}{d x} (sec (sin (x)))

y^{^{''}} + 5 y^{^{'}} - 6 y = 0, y (0) = 2, y^{^{'}} (0) = - 1

What is the integral of sin(3x)+10cos(x) ?
The integral of sin(3x)+10cos(x) is -1/3 cos(3x)+10sin(x)+C