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

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

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

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

2 1 + t + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= 2 u^{\frac{1}{2}}

Substitute back

u = 1 + t

= 2 (1 + t)^{\frac{1}{2}}

Apply radical rule:

a^{\frac{1}{n}} = n a

= 2 1 + t

Add a constant to the solution

= 2 1 + t + C

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