What is the integral of 3e^{4x}-5cos(6x)+7 ?

The integral of 3e^{4x}-5cos(6x)+7 is 3/4 e^{4x}-5/6 sin(6x)+7x+C

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integral of 3e^{4x}-5cos(6x)+7

\int 3 e^{4 x} - 5 cos (6 x) + 7 d x

\frac{3}{4} e^{4 x} - \frac{5}{6} sin (6 x) + 7 x + C

Solution steps

\int 3 e^{4 x} - 5 cos (6 x) + 7 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^{4 x} d x - \int 5 cos (6 x) d x + \int 7 d x

\int 3 e^{4 x} d x = \frac{3}{4} e^{4 x}

\int 5 cos (6 x) d x = \frac{5}{6} sin (6 x)

\int 7 d x = 7 x

= \frac{3}{4} e^{4 x} - \frac{5}{6} sin (6 x) + 7 x

Add a constant to the solution

= \frac{3}{4} e^{4 x} - \frac{5}{6} sin (6 x) + 7 x + C

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What is the integral of 3e^{4x}-5cos(6x)+7 ?
The integral of 3e^{4x}-5cos(6x)+7 is 3/4 e^{4x}-5/6 sin(6x)+7x+C