What is the integral of cos(3t)+sin(4t) ?

The integral of cos(3t)+sin(4t) is 1/3 sin(3t)-1/4 cos(4t)+C

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integral of cos(3t)+sin(4t)

\int cos (3 t) + sin (4 t) d t

\frac{1}{3} sin (3 t) - \frac{1}{4} cos (4 t) + C

Solution steps

\int cos (3 t) + sin (4 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 cos (3 t) d t + \int sin (4 t) d t

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

\int sin (4 t) d t = - \frac{1}{4} cos (4 t)

= \frac{1}{3} sin (3 t) - \frac{1}{4} cos (4 t)

Add a constant to the solution

= \frac{1}{3} sin (3 t) - \frac{1}{4} cos (4 t) + C

\frac{d}{d x} (x^{3} + \frac{1}{x})

\int_{0}^{\infty} 70 \frac{e ^{x}}{e ^{2 x} + 3} d x

7 e^{x} cos (x)

(8 + x) y^{^{'}} = 3 y

What is the integral of cos(3t)+sin(4t) ?
The integral of cos(3t)+sin(4t) is 1/3 sin(3t)-1/4 cos(4t)+C