What is the integral of (x+1)/(x^2+2x-3) ?

The integral of (x+1)/(x^2+2x-3) is 1/2 ln|x^2+2x-3|+C

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integral of (x+1)/(x^2+2x-3)

\int \frac{x + 1}{x ^{2} + 2 x - 3} d x

\frac{1}{2} ln x^{2} + 2 x - 3 + C

Solution steps

\int \frac{x + 1}{x ^{2} + 2 x - 3} d x

Apply u-substitution

: \int \frac{1}{2 u} d u

= \int \frac{1}{2 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} ln ∣ u ∣

Substitute back

u = x^{2} + 2 x - 3

= \frac{1}{2} ln x^{2} + 2 x - 3

Add a constant to the solution

= \frac{1}{2} ln x^{2} + 2 x - 3 + C

\frac{\partial}{\partial x} (x^{3} + 8 y^{3} - 6 x y + 5)

x \to - 1 - lim (x^{3} - 3)

\frac{d}{d x} (3 a x^{2} + 2 b x + c)

\int (4 x^{2} - 2) x d x

y = sin (sin (x)), (3 π, 0)

What is the integral of (x+1)/(x^2+2x-3) ?
The integral of (x+1)/(x^2+2x-3) is 1/2 ln|x^2+2x-3|+C