What is the integral from 2 to 4 of 5^{4x} ?

The integral from 2 to 4 of 5^{4x} is (625^4-390625)/(4ln(5))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 2 to 4 of 5^{4x}

\int_{2}^{4} 5^{4 x} d x

\frac{62 5 ^{4} - 390625}{4 ln ( 5 )}

Decimal

23701986081.778694

Solution steps

\int_{2}^{4} 5^{4 x} d x

Simplify

5^{4 x} : 62 5^{x}

= \int_{2}^{4} 62 5^{x} d x

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

= [\frac{62 5 ^{x}}{ln ( 625 )}]_{2}^{4}

Simplify

ln (625) : 4 ln (5)

= [\frac{62 5 ^{x}}{4 ln ( 5 )}]_{2}^{4}

Compute the boundaries:

\frac{62 5 ^{4} - 390625}{4 ln ( 5 )}

= \frac{62 5 ^{4} - 390625}{4 ln ( 5 )}

\int_{1}^{4} 8 x^{3} - 2 x + e^{x} d x

\int_{- 5 π}^{4 π} cos^{2} (x) d x

\int_{- 3}^{1} 6 x^{2} + 2 x d x

\int_{0}^{6} 3 x 36 - x^{2} d x

\int_{3}^{5} π (x - 3)^{3} d x

What is the integral from 2 to 4 of 5^{4x} ?
The integral from 2 to 4 of 5^{4x} is (625^4-390625)/(4ln(5))