What is the integral from 0 to 1 of 7^{3x} ?

The integral from 0 to 1 of 7^{3x} is (114)/(ln(7))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 1 of 7^{3x}

\int_{0}^{1} 7^{3 x} d x

\frac{114}{ln ( 7 )}

Decimal Notation

58.58441 \dots

Solution steps

\int_{0}^{1} 7^{3 x} d x

Simplify

7^{3 x} : 34 3^{x}

= \int_{0}^{1} 34 3^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

= [\frac{34 3 ^{x}}{ln ( 343 )}]_{0}^{1}

Simplify

ln (343) : 3 ln (7)

= [\frac{34 3 ^{x}}{3 ln ( 7 )}]_{0}^{1}

Compute the boundaries:

\frac{114}{ln ( 7 )}

= \frac{114}{ln ( 7 )}

\int \frac{( ln ( x ) - 1 ) ^{2}}{x} d x

y = \frac{x}{3} + \frac{3 x ^{2}}{2}

x \to 0 lim (\frac{( 1 )}{x ^{2}})

\int \frac{( x ^{2} - x + 12 )}{x ^{3} + 6 x} d x

What is the integral from 0 to 1 of 7^{3x} ?
The integral from 0 to 1 of 7^{3x} is (114)/(ln(7))