What is the integral of a^xx ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of a^xx

\int a^{x} x d x

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

Solution steps

\int a^{x} x d x

Apply Integration By Parts

: \frac{a ^{x} x}{ln ( a )} - \int \frac{a ^{x}}{ln ( a )} d x

= \frac{a ^{x} x}{ln ( a )} - \int \frac{a ^{x}}{ln ( a )} d x

\int \frac{a ^{x}}{ln ( a )} d x = \frac{a ^{x}}{ln ^{2} ( a )}

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

Add a constant to the solution

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

y = 2 x^{2}, y = 8 x - 2 x^{2}

\frac{\partial}{\partial y} (x^{2} + y^{2} - 13)

f (x) = - x^{2} - 7 x + 44, at x = 2

\int - e^{3 x} d x

\frac{2 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}}

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