What is the integral of x^25^x ?

The integral of x^25^x is (5^xx^2)/(ln(5))-2/(ln(5))((5^xx)/(ln(5))-(5^x)/(ln^2(5)))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^25^x

\int x^{2} 5^{x} d x

\frac{5 ^{x} x ^{2}}{ln ( 5 )} - \frac{2}{ln ( 5 )} (\frac{5 ^{x} x}{ln ( 5 )} - \frac{5 ^{x}}{ln ^{2} ( 5 )}) + C

Solution steps

\int x^{2} \cdot 5^{x} d x

Apply Integration By Parts

: \frac{5 ^{x} x ^{2}}{ln ( 5 )} - \int \frac{2 \cdot 5 ^{x} x}{ln ( 5 )} d x

= \frac{5 ^{x} x ^{2}}{ln ( 5 )} - \int \frac{2 \cdot 5 ^{x} x}{ln ( 5 )} d x

\int \frac{2 \cdot 5 ^{x} x}{ln ( 5 )} d x = \frac{2}{ln ( 5 )} (\frac{5 ^{x} x}{ln ( 5 )} - \frac{5 ^{x}}{ln ^{2} ( 5 )})

= \frac{5 ^{x} x ^{2}}{ln ( 5 )} - \frac{2}{ln ( 5 )} (\frac{5 ^{x} x}{ln ( 5 )} - \frac{5 ^{x}}{ln ^{2} ( 5 )})

Add a constant to the solution

= \frac{5 ^{x} x ^{2}}{ln ( 5 )} - \frac{2}{ln ( 5 )} (\frac{5 ^{x} x}{ln ( 5 )} - \frac{5 ^{x}}{ln ^{2} ( 5 )}) + C

\int \frac{10}{x} d x

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

x \to 0 lim (\frac{3}{x ^{2} + x} - \frac{3}{x})

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

\frac{d x}{d t} = 12 - \frac{27 x}{900 - 15 t}

What is the integral of x^25^x ?
The integral of x^25^x is (5^xx^2)/(ln(5))-2/(ln(5))((5^xx)/(ln(5))-(5^x)/(ln^2(5)))+C