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

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

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

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

2 t + 1 + C

Solution steps

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

= 2 t + 1

Add a constant to the solution

= 2 t + 1 + C

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

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\int \frac{1}{4 x ^{3} - x} d x

\int \frac{1}{cos ^{2} ( x ) 1 + tan ^{2} ( x )} d x

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