What is the integral of (2x+7)/(x+3) ?

The integral of (2x+7)/(x+3) is 2(x+3)+ln|x+3|+C

Popular >

integral of (2x+7)/(x+3)

\int \frac{2 x + 7}{x + 3} d x

2 (x + 3) + ln ∣ x + 3 ∣ + C

Solution steps

\int \frac{2 x + 7}{x + 3} d x

Apply u-substitution

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

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

Expand

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

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

\int 2 d u = 2 u

\int \frac{1}{u} d u = ln ∣ u ∣

= 2 u + ln ∣ u ∣

Substitute back

u = x + 3

= 2 (x + 3) + ln ∣ x + 3 ∣

Add a constant to the solution

= 2 (x + 3) + ln ∣ x + 3 ∣ + C

\int \frac{1}{x ^{2} x ^{2} - 10} d x

\frac{s + 1}{( s + 6 ) ^{2} ( s + 2 )}

\frac{8}{3 x + 3}

f (x) = \frac{6 cos ( x )}{7 - 9 cos ( x )}

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

What is the integral of (2x+7)/(x+3) ?
The integral of (2x+7)/(x+3) is 2(x+3)+ln|x+3|+C