What is the integral of x*7^x ?

The integral of x*7^x is (7^xx)/(ln(7))-(7^x)/(ln^2(7))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x*7^x

\int x \cdot 7^{x} d x

\frac{7 ^{x} x}{ln ( 7 )} - \frac{7 ^{x}}{ln ^{2} ( 7 )} + C

Solution steps

\int x \cdot 7^{x} d x

Apply Integration By Parts

: \frac{7 ^{x} x}{ln ( 7 )} - \int \frac{7 ^{x}}{ln ( 7 )} d x

= \frac{7 ^{x} x}{ln ( 7 )} - \int \frac{7 ^{x}}{ln ( 7 )} d x

\int \frac{7 ^{x}}{ln ( 7 )} d x = \frac{7 ^{x}}{ln ^{2} ( 7 )}

= \frac{7 ^{x} x}{ln ( 7 )} - \frac{7 ^{x}}{ln ^{2} ( 7 )}

Add a constant to the solution

= \frac{7 ^{x} x}{ln ( 7 )} - \frac{7 ^{x}}{ln ^{2} ( 7 )} + C

\int e^{\frac{1}{7} x} d x

\int (4 x^{3} + 8 x + 9) d x

\int (2 e^{x} + x^{2}) d x

\int x^{5} in x d x

\int \frac{12 x}{1 + 4} d x

What is the integral of x*7^x ?
The integral of x*7^x is (7^xx)/(ln(7))-(7^x)/(ln^2(7))+C