What is the integral from 0 to 2 of e^x+1/(x^2+1) ?

The integral from 0 to 2 of e^x+1/(x^2+1) is e^2-1+arctan(2)

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integral from 0 to 2 of e^x+1/(x^2+1)

\int_{0}^{2} e^{x} + \frac{1}{x ^{2} + 1} d x

e^{2} - 1 + arctan (2)

Decimal Notation

7.49620 \dots

Solution steps

\int_{0}^{2} e^{x} + \frac{1}{x ^{2} + 1} 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_{0}^{2} e^{x} d x + \int_{0}^{2} \frac{1}{x ^{2} + 1} d x

\int_{0}^{2} e^{x} d x = e^{2} - 1

\int_{0}^{2} \frac{1}{x ^{2} + 1} d x = arctan (2)

= e^{2} - 1 + arctan (2)

\int_{2}^{5} - 2 x^{2} + 12 x - 17 d x

\int_{1}^{2} e^{- l n (x)} d x

\int_{4}^{13} \frac{1}{x - 4} d x

\int_{3}^{4} (x - 4)^{3} - (x - 4) d x

\int_{r^{1}}^{r^{2}} \frac{1}{r ^{2}} d r

What is the integral from 0 to 2 of e^x+1/(x^2+1) ?
The integral from 0 to 2 of e^x+1/(x^2+1) is e^2-1+arctan(2)