What is the integral of (sqrt(x)-3)/(sqrt(x)+1) ?

The integral of (sqrt(x)-3)/(sqrt(x)+1) is -8(sqrt(x)+1-ln|sqrt(x)+1|)+x+C

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integral of (sqrt(x)-3)/(sqrt(x)+1)

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

- 8 (x + 1 - ln x + 1) + x + C

Solution steps

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

\frac{x - 3}{x + 1} = - \frac{4}{x + 1} + 1

= \int - \frac{4}{x + 1} + 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 \frac{4}{x + 1} d x + \int 1 d x

\int \frac{4}{x + 1} d x = 8 (x + 1 - ln x + 1)

\int 1 d x = x

= - 8 (x + 1 - ln x + 1) + x

Add a constant to the solution

= - 8 (x + 1 - ln x + 1) + x + C

\frac{d}{d x} (7 x + 3)

x^{- \frac{1}{2}}

n \to \infty lim (\frac{3 n ^{0.4 + 1} + 7 n}{3 n ^{0.4} + 7 n})

y^{^{''}} + 5 y^{^{'}} = e^{- t}, y (0) = - 0, y^{^{'}} (0) = 1

\int \frac{- y}{cot ( x )} d x

What is the integral of (sqrt(x)-3)/(sqrt(x)+1) ?
The integral of (sqrt(x)-3)/(sqrt(x)+1) is -8(sqrt(x)+1-ln|sqrt(x)+1|)+x+C