What is the integral of (2e^{x-3}+3sin(x)+7/(1+x^2)) ?

The integral of (2e^{x-3}+3sin(x)+7/(1+x^2)) is 2e^{x-3}-3cos(x)+7arctan(x)+C

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integral of (2e^{x-3}+3sin(x)+7/(1+x^2))

\int (2 e^{x - 3} + 3 sin (x) + \frac{7}{1 + x ^{2}}) d x

2 e^{x - 3} - 3 cos (x) + 7 arctan (x) + C

Solution steps

\int 2 e^{x - 3} + 3 sin (x) + \frac{7}{1 + x ^{2}} 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 2 e^{x - 3} d x + \int 3 sin (x) d x + \int \frac{7}{1 + x ^{2}} d x

\int 2 e^{x - 3} d x = 2 e^{x - 3}

\int 3 sin (x) d x = - 3 cos (x)

\int \frac{7}{1 + x ^{2}} d x = 7 arctan (x)

= 2 e^{x - 3} - 3 cos (x) + 7 arctan (x)

Add a constant to the solution

= 2 e^{x - 3} - 3 cos (x) + 7 arctan (x) + C

What is the integral of (2e^{x-3}+3sin(x)+7/(1+x^2)) ?
The integral of (2e^{x-3}+3sin(x)+7/(1+x^2)) is 2e^{x-3}-3cos(x)+7arctan(x)+C