What is the integral of 5cos(3x)-4sin(5x) ?

The integral of 5cos(3x)-4sin(5x) is 5/3 sin(3x)+4/5 cos(5x)+C

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integral of 5cos(3x)-4sin(5x)

\int 5 cos (3 x) - 4 sin (5 x) d x

\frac{5}{3} sin (3 x) + \frac{4}{5} cos (5 x) + C

Solution steps

\int 5 cos (3 x) - 4 sin (5 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 5 cos (3 x) d x - \int 4 sin (5 x) d x

\int 5 cos (3 x) d x = \frac{5}{3} sin (3 x)

\int 4 sin (5 x) d x = - \frac{4}{5} cos (5 x)

= \frac{5}{3} sin (3 x) - (- \frac{4}{5} cos (5 x))

Simplify

= \frac{5}{3} sin (3 x) + \frac{4}{5} cos (5 x)

Add a constant to the solution

= \frac{5}{3} sin (3 x) + \frac{4}{5} cos (5 x) + C

lo g_{5} (x)

\frac{1}{3} x^{\frac{1}{2}} - x^{\frac{3}{2}}, x = 0, x = \frac{1}{3}

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

x \to 4 - lim (\frac{7}{x - 4})

\frac{\partial}{\partial x} (\frac{6}{x ^{4}})

What is the integral of 5cos(3x)-4sin(5x) ?
The integral of 5cos(3x)-4sin(5x) is 5/3 sin(3x)+4/5 cos(5x)+C