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

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

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integral of (cos(3x)-sin(x))

\int (cos (3 x) - sin (x)) d x

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

Solution steps

\int cos (3 x) - sin (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 cos (3 x) d x - \int sin (x) d x

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

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

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

Simplify

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

Add a constant to the solution

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

\int_{- \infty}^{0} \frac{1}{2 - 5 x} d x

y = x^{3} - 2 x + 1

\int \frac{1}{( 9 - x ) ^{\frac{3}{2}}} d x

\int sin (\frac{3}{4}) x cos^{2} (\frac{3}{4}) x d x

n = 1 (1 - \frac{1}{n}) \sum \infty n^{2}

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