What is the integral of cos(t)-5sin(t) ?

The integral of cos(t)-5sin(t) is sin(t)+5cos(t)+C

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integral of cos(t)-5sin(t)

\int cos (t) - 5 sin (t) d t

sin (t) + 5 cos (t) + C

Solution steps

\int cos (t) - 5 sin (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 (t) d t - \int 5 sin (t) d t

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

\int 5 sin (t) d t = - 5 cos (t)

= sin (t) - (- 5 cos (t))

Simplify

= sin (t) + 5 cos (t)

Add a constant to the solution

= sin (t) + 5 cos (t) + C

x \to 0 + lim (x ln (tan (5 x)))

4 s

f (x) = \frac{2}{x}, at x = - 9

\frac{d}{d x} ((x^{2} + 2 x) e^{x})

\int_{- 1}^{1} cos (nπ x) d x

What is the integral of cos(t)-5sin(t) ?
The integral of cos(t)-5sin(t) is sin(t)+5cos(t)+C