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

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

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

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

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

Decimal Notation

4.52786 \dots

Solution steps

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

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

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

\int_{0}^{1} 1 d x = 1

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

Combine the fractions

1 + \frac{1}{3} : \frac{4}{3}

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

\frac{d}{d x} (\frac{1 - x e ^{x}}{1 + e ^{x}})

\frac{\partial}{\partial x} (x^{2} y^{2} - y^{3} + 3 x^{4} + 5)

\int_{0}^{4} 10 x d x

f (x) = \frac{1}{x ^{2}}

y^{^{''}} + 2 k^{2} y^{^{'}} + k^{4} y = 0

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