What is the integral of (sin(a)x-e^{x/b}) ?

The integral of (sin(a)x-e^{x/b}) is 1/2 x^2sin(a)-be^{x/b}+C

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integral of (sin(a)x-e^{x/b})

\int (sin (a) x - e^{\frac{x}{b}}) d x

\frac{1}{2} x^{2} sin (a) - b e^{\frac{x}{b}} + C

Solution steps

\int sin (a) x - e^{\frac{x}{b}} 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 sin (a) x d x - \int e^{\frac{x}{b}} d x

\int sin (a) x d x = \frac{1}{2} x^{2} sin (a)

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

= \frac{1}{2} x^{2} sin (a) - b e^{\frac{x}{b}}

Add a constant to the solution

= \frac{1}{2} x^{2} sin (a) - b e^{\frac{x}{b}} + C

csc^{2} (x)

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What is the integral of (sin(a)x-e^{x/b}) ?
The integral of (sin(a)x-e^{x/b}) is 1/2 x^2sin(a)-be^{x/b}+C