What is the integral of (3e^x+5sin(x)) ?

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

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integral of (3e^x+5sin(x))

\int (3 e^{x} + 5 sin (x)) d x

3 e^{x} - 5 cos (x) + C

Solution steps

\int 3 e^{x} + 5 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 3 e^{x} d x + \int 5 sin (x) d x

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

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

= 3 e^{x} - 5 cos (x)

Add a constant to the solution

= 3 e^{x} - 5 cos (x) + C

\int_{1}^{2} x sin (x^{2}) d x

\frac{d}{d x} (\frac{72}{x})

\int_{0}^{π} (cos (2 x))^{4} d x

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

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

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