What is the integral of e^x+4sin(x) ?

The integral of e^x+4sin(x) is e^x-4cos(x)+C

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integral of e^x+4sin(x)

\int e^{x} + 4 sin (x) d x

e^{x} - 4 cos (x) + C

Solution steps

\int e^{x} + 4 sin (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 e^{x} d x + \int 4 sin (x) d x

\int e^{x} d x = e^{x}

\int 4 sin (x) d x = - 4 cos (x)

= e^{x} - 4 cos (x)

Add a constant to the solution

= e^{x} - 4 cos (x) + C

\int \frac{1}{tan ^{3} ( x )} d x

\int \frac{x ^{3}}{4 + x ^{2}} d x

\int \frac{x ^{2}}{( x - 2 ) ( 4 - x )} d x

\int cos (x) (sin (x) + 1)^{3} d x

\int \frac{2}{3 x ^{3}} d x

What is the integral of e^x+4sin(x) ?
The integral of e^x+4sin(x) is e^x-4cos(x)+C