What is the integral of 3e^{5x}-3cos(4x) ?

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

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integral of 3e^{5x}-3cos(4x)

\int 3 e^{5 x} - 3 cos (4 x) d x

\frac{3}{5} e^{5 x} - \frac{3}{4} sin (4 x) + C

Solution steps

\int 3 e^{5 x} - 3 cos (4 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 3 e^{5 x} d x - \int 3 cos (4 x) d x

\int 3 e^{5 x} d x = \frac{3}{5} e^{5 x}

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

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

Add a constant to the solution

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

x \to 0 lim (- (ln (x)))

t \to 0 lim (\frac{e ^{3 t} - 1}{t})

x \to \infty + lim (\frac{1}{x} + 4)

\frac{d}{d x} (\frac{6}{x - 1})

\int_{0}^{1} 3 - x^{2} d x

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