What is the integral of (3t+2)/(t+1) ?

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

Popular >

integral of (3t+2)/(t+1)

\int \frac{3 t + 2}{t + 1} d t

3 (t + 1) - ln ∣ t + 1 ∣ + C

Solution steps

\int \frac{3 t + 2}{t + 1} d t

Apply u-substitution

: \int \frac{3 u - 1}{u} d u

= \int \frac{3 u - 1}{u} d u

Expand

\frac{3 u - 1}{u} : 3 - \frac{1}{u}

= \int 3 - \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 3 d u - \int \frac{1}{u} d u

\int 3 d u = 3 u

\int \frac{1}{u} d u = ln ∣ u ∣

= 3 u - ln ∣ u ∣

Substitute back

u = t + 1

= 3 (t + 1) - ln ∣ t + 1 ∣

Add a constant to the solution

= 3 (t + 1) - ln ∣ t + 1 ∣ + C

\frac{d}{d x} (e)

\frac{12800}{1 + 10 e ^{- 0.5 x}}

\frac{d}{d x} (7 - \frac{1}{3} x)

\int_{0}^{1} (x^{2} + 5) (e^{- x}) d x

\frac{d}{d θ} (θ^{2})

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