What is the integral of 1/(sqrt(1+t)) ?

The integral of 1/(sqrt(1+t)) is 2sqrt(1+t)+C

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integral of 1/(sqrt(1+t))

\int \frac{1}{1 + t} d t

2 1 + t + C

Solution steps

\int \frac{1}{1 + t} d t

Apply u-substitution

: \int 2 d u

= \int 2 d u

Integral of a constant:

\int a d x = a x

= 2 u

Substitute back

u = 1 + t

= 2 1 + t

Add a constant to the solution

= 2 1 + t + C

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What is the integral of 1/(sqrt(1+t)) ?
The integral of 1/(sqrt(1+t)) is 2sqrt(1+t)+C