What is the integral of sin(2t)+cos(t) ?

The integral of sin(2t)+cos(t) is -1/2 cos(2t)+sin(t)+C

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integral of sin(2t)+cos(t)

\int sin (2 t) + cos (t) d t

- \frac{1}{2} cos (2 t) + sin (t) + C

Solution steps

\int sin (2 t) + 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 sin (2 t) d t + \int cos (t) d t

\int sin (2 t) d t = - \frac{1}{2} cos (2 t)

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

= - \frac{1}{2} cos (2 t) + sin (t)

Add a constant to the solution

= - \frac{1}{2} cos (2 t) + sin (t) + C

\int (1 + 4 x^{2}) d x

\frac{d}{d x} (\frac{11}{ln ( x )})

x \frac{d y}{d x} + y = sin (x)

f (x) = 2 x^{2} - 6 x + 6, at x = 7

\frac{\partial}{\partial x} (x \cdot y \cdot ln (x^{2} + y^{2}))

What is the integral of sin(2t)+cos(t) ?
The integral of sin(2t)+cos(t) is -1/2 cos(2t)+sin(t)+C