What is the integral of 5cos(3z)+2/(e^{4z)} ?

The integral of 5cos(3z)+2/(e^{4z)} is 5/3 sin(3z)-1/2 e^{-4z}+C

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integral of 5cos(3z)+2/(e^{4z)}

\int 5 cos (3 z) + \frac{2}{e ^{4 z}} d z

\frac{5}{3} sin (3 z) - \frac{1}{2} e^{- 4 z} + C

Solution steps

\int 5 cos (3 z) + \frac{2}{e ^{4 z}} d z

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 z) d z + \int \frac{2}{e ^{4 z}} d z

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

\int \frac{2}{e ^{4 z}} d z = - \frac{1}{2} e^{- 4 z}

= \frac{5}{3} sin (3 z) - \frac{1}{2} e^{- 4 z}

Add a constant to the solution

= \frac{5}{3} sin (3 z) - \frac{1}{2} e^{- 4 z} + C

2 t y^{^{'}} + y = e^{t}

\frac{\partial}{\partial y} (x^{2} - x - 12 y + 1)

\int_{0}^{27} \frac{4}{x ^{\frac{2}{3}}} d x

\int 5 x ln (4 x) d x

f (x) = x^{2} + 3 x - 7

What is the integral of 5cos(3z)+2/(e^{4z)} ?
The integral of 5cos(3z)+2/(e^{4z)} is 5/3 sin(3z)-1/2 e^{-4z}+C