What is the integral from 1 to e of (6^x-2^x) ?

The integral from 1 to e of (6^x-2^x) is (6^e-6)/(ln(6))-(2^e-2)/(ln(2))

Popular >

integral from 1 to e of (6^x-2^x)

\int_{1}^{e} (6^{x} - 2^{x}) d x

\frac{6 ^{e} - 6}{ln ( 6 )} - \frac{2 ^{e} - 2}{ln ( 2 )}

Decimal

62.81290 \dots

Solution steps

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

\int_{1}^{e} 6^{x} d x = \frac{6 ^{e} - 6}{ln ( 6 )}

\int_{1}^{e} 2^{x} d x = \frac{2 ^{e} - 2}{ln ( 2 )}

= \frac{6 ^{e} - 6}{ln ( 6 )} - \frac{2 ^{e} - 2}{ln ( 2 )}

\int_{\frac{π}{3}}^{\frac{π}{4}} sin (x) d x

\int_{\frac{1}{2}}^{1} sin (nπ x) d x

\int_{1}^{x} ln (7 + t^{2}) d t

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

\int_{- 1}^{1} 3 - ∣ x ∣ d x

What is the integral from 1 to e of (6^x-2^x) ?
The integral from 1 to e of (6^x-2^x) is (6^e-6)/(ln(6))-(2^e-2)/(ln(2))