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Popular >

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

Solution

integral

\frac{x + 3}{x - 2}

Solution

x - 2 + 5 ln ∣ x - 2 ∣ + C

Solution steps

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

Apply u-substitution

: \int \frac{u + 5}{u} d u

= \int \frac{u + 5}{u} d u

Expand

\frac{u + 5}{u} : 1 + \frac{5}{u}

= \int 1 + \frac{5}{u} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d u + \int \frac{5}{u} d u

\int 1 d u = u

\int \frac{5}{u} d u = 5 ln ∣ u ∣

= u + 5 ln ∣ u ∣

Substitute back

u = x - 2

= x - 2 + 5 ln ∣ x - 2 ∣

Add a constant to the solution

= x - 2 + 5 ln ∣ x - 2 ∣ + C

Popular Examples

integral of e^{(1-x)}

\int e^{(1 - x)} d x

integral of 1/(ssqrt(s^2-9))

\int \frac{1}{s s ^{2} - 9} d s

integral of (-4x^6+2x^5-3x^3+3)

\int (- 4 x^{6} + 2 x^{5} - 3 x^{3} + 3) d x

integral of (3x^3+4x-3)

\int (3 x^{3} + 4 x - 3) d x

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

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

Frequently Asked Questions (FAQ)

What is the integral of (x+3)/(x-2) ?
The integral of (x+3)/(x-2) is x-2+5ln|x-2|+C