What is the integral from 1 to ln(8) of 6x+e^x ?

The integral from 1 to ln(8) of 6x+e^x is 27ln^2(2)+5-e

Popular >

integral from 1 to ln(8) of 6x+e^x

\int_{1}^{l n (8)} 6 x + e^{x} d x

27 ln^{2} (2) + 5 - e

Decimal

15.25394 \dots

Solution steps

\int_{1}^{l n (8)} 6 x + 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_{1}^{l n (8)} 6 x d x + \int_{1}^{l n (8)} e^{x} d x

\int_{1}^{l n (8)} 6 x d x = 3 (9 ln^{2} (2) - 1)

\int_{1}^{l n (8)} e^{x} d x = 8 - e

= 3 (9 ln^{2} (2) - 1) + 8 - e

Simplify

3 (9 ln^{2} (2) - 1) + 8 - e : 27 ln^{2} (2) + 5 - e

= 27 ln^{2} (2) + 5 - e

\int_{0}^{\frac{π}{2}} \frac{1}{2 + sin ( x )} d x

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

\int_{- π}^{0} x cos (n x) d x

\int_{0}^{\frac{π}{4}} cos^{7} (2 x) d x

\int_{- 2}^{4} (1 - x - 4 x^{3} + 2 x^{5}) d x

What is the integral from 1 to ln(8) of 6x+e^x ?
The integral from 1 to ln(8) of 6x+e^x is 27ln^2(2)+5-e