What is the integral from 0 to 1 of (7x^e+5e^x) ?

The integral from 0 to 1 of (7x^e+5e^x) is 7/(e+1)+5(e-1)

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integral from 0 to 1 of (7x^e+5e^x)

\int_{0}^{1} (7 x^{e} + 5 e^{x}) d x

\frac{7}{e + 1} + 5 (e - 1)

Decimal

10.47399 \dots

Solution steps

\int_{0}^{1} 7 x^{e} + 5 e^{x} 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} 7 x^{e} d x + \int_{0}^{1} 5 e^{x} d x

\int_{0}^{1} 7 x^{e} d x = \frac{7}{e + 1}

\int_{0}^{1} 5 e^{x} d x = 5 (e - 1)

= \frac{7}{e + 1} + 5 (e - 1)

\int_{- 3}^{1} g (x) d x

\int_{0}^{1} (- x^{2} - 3 x) d x

\int_{- 5}^{5} (5 + 25 - x^{2}) d x

\int_{0}^{1 - y^{2}} c x d x

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

What is the integral from 0 to 1 of (7x^e+5e^x) ?
The integral from 0 to 1 of (7x^e+5e^x) is 7/(e+1)+5(e-1)