What is the integral from 1 to infinity of sqrt(x+1) ?

The integral from 1 to infinity of sqrt(x+1) is diverges

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integral from 1 to infinity of sqrt(x+1)

\int_{1}^{\infty} x + 1 d x

diverges

Solution steps

\int_{1}^{\infty} x + 1 d x

Compute the indefinite integral:

\int x + 1 d x = \frac{2}{3} (x + 1)^{\frac{3}{2}} + C

Compute the boundaries:

\int_{1}^{\infty} x + 1 d x =

diverges

= diverges

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What is the integral from 1 to infinity of sqrt(x+1) ?
The integral from 1 to infinity of sqrt(x+1) is diverges