What is the integral of 1+3ln(x+1) ?

The integral of 1+3ln(x+1) is -2x+3xln(x+1)+3ln(x+1)-3+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1+3ln(x+1)

\int 1 + 3 ln (x + 1) d x

- 2 x + 3 x ln (x + 1) + 3 ln (x + 1) - 3 + C

Solution steps

\int 1 + 3 ln (x + 1) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d x + \int 3 ln (x + 1) d x

\int 1 d x = x

\int 3 ln (x + 1) d x = 3 (x ln (x + 1) + ln (x + 1) - x - 1)

= x + 3 (x ln (x + 1) + ln (x + 1) - x - 1)

Simplify

x + 3 (x ln (x + 1) + ln (x + 1) - x - 1) : - 2 x + 3 x ln (x + 1) + 3 ln (x + 1) - 3

= - 2 x + 3 x ln (x + 1) + 3 ln (x + 1) - 3

Add a constant to the solution

= - 2 x + 3 x ln (x + 1) + 3 ln (x + 1) - 3 + C

\int \frac{1}{( 5 x ) ^{3}} d x

\int (e^{x + 3} + e^{x - 3}) d x

\int 4 x^{7} x^{4} + 1 d x

\int 2 sin (3 x) e^{- x} d x

\int 2^{7 x + 3} d x

What is the integral of 1+3ln(x+1) ?
The integral of 1+3ln(x+1) is -2x+3xln(x+1)+3ln(x+1)-3+C