What is the integral from 0 to 1 of e^{2x}+3/(x^2+1) ?

The integral from 0 to 1 of e^{2x}+3/(x^2+1) is (e^2-1)/2+(3pi)/4

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integral from 0 to 1 of e^{2x}+3/(x^2+1)

\int_{0}^{1} e^{2 x} + \frac{3}{x ^{2} + 1} d x

\frac{e ^{2} - 1}{2} + \frac{3 π}{4}

Decimal

5.55072 \dots

Solution steps

\int_{0}^{1} e^{2 x} + \frac{3}{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}^{1} e^{2 x} d x + \int_{0}^{1} \frac{3}{x ^{2} + 1} d x

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

\int_{0}^{1} \frac{3}{x ^{2} + 1} d x = \frac{3 π}{4}

= \frac{e ^{2} - 1}{2} + \frac{3 π}{4}

What is the integral from 0 to 1 of e^{2x}+3/(x^2+1) ?
The integral from 0 to 1 of e^{2x}+3/(x^2+1) is (e^2-1)/2+(3pi)/4