What is the integral from 0 to 1 of 2e^{x/3+4}+5 ?

The integral from 0 to 1 of 2e^{x/3+4}+5 is 6e^4(\sqrt[3]{e}-1)+5

Popular >

integral from 0 to 1 of 2e^{x/3+4}+5

\int_{0}^{1} 2 e^{\frac{x}{3} + 4} + 5 d x

6 e^{4} (3 e - 1) + 5

Decimal

134.59823 \dots

Solution steps

\int_{0}^{1} 2 e^{\frac{x}{3} + 4} + 5 d x

e^{\frac{x}{3} + 4} = e^{4} e^{\frac{x}{3}}

= \int_{0}^{1} 2 e^{4} e^{\frac{x}{3}} + 5 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} 2 e^{4} e^{\frac{x}{3}} d x + \int_{0}^{1} 5 d x

\int_{0}^{1} 2 e^{4} e^{\frac{x}{3}} d x = 6 e^{4} (3 e - 1)

\int_{0}^{1} 5 d x = 5

= 6 e^{4} (3 e - 1) + 5

\int_{0}^{x} x^{2} d x

\int_{0}^{\frac{π}{4}} \frac{1}{cos ^{2} ( x )} d x

\int_{1}^{\infty} x^{2} e^{- x} d x

\int_{- 2}^{3} e^{\frac{x}{2}} d x

\int_{1}^{6} \frac{e ^{\frac{1}{x}}}{x ^{2}} d x

What is the integral from 0 to 1 of 2e^{x/3+4}+5 ?
The integral from 0 to 1 of 2e^{x/3+4}+5 is 6e^4(\sqrt[3]{e}-1)+5