What is the integral of 7^{ln(x)} ?

The integral of 7^{ln(x)} is 7^{ln(x)}x-1/(ln(7)+1)ln(7)x^{ln(7)+1}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 7^{ln(x)}

\int 7^{l n (x)} d x

7^{l n (x)} x - \frac{1}{ln ( 7 ) + 1} ln (7) x^{l n (7) + 1} + C

Solution steps

\int 7^{l n (x)} d x

Apply Integration By Parts

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

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

\int ln (7) x^{l n (7)} d x = \frac{1}{ln ( 7 ) + 1} ln (7) x^{l n (7) + 1}

= 7^{l n (x)} x - \frac{1}{ln ( 7 ) + 1} ln (7) x^{l n (7) + 1}

Add a constant to the solution

= 7^{l n (x)} x - \frac{1}{ln ( 7 ) + 1} ln (7) x^{l n (7) + 1} + C

\int 8 (\frac{sin ( 2 x )}{sin ( x )}) d x

\int \frac{24}{1 + 25 x ^{2}} d x

\int 27 sin (x) d x

\int \frac{( x + 1 )}{x ^{3}} d x

\int \frac{1}{2 x 4 x ^{2} - 9} d x

What is the integral of 7^{ln(x)} ?
The integral of 7^{ln(x)} is 7^{ln(x)}x-1/(ln(7)+1)ln(7)x^{ln(7)+1}+C