What is the integral of (5t-2)/(t+1) ?

The integral of (5t-2)/(t+1) is 5(t+1)-7ln|t+1|+C

Popular >

integral of (5t-2)/(t+1)

\int \frac{5 t - 2}{t + 1} d t

5 (t + 1) - 7 ln ∣ t + 1 ∣ + C

Solution steps

\int \frac{5 t - 2}{t + 1} d t

Apply u-substitution

: \int \frac{5 u - 7}{u} d u

= \int \frac{5 u - 7}{u} d u

Expand

\frac{5 u - 7}{u} : 5 - \frac{7}{u}

= \int 5 - \frac{7}{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 5 d u - \int \frac{7}{u} d u

\int 5 d u = 5 u

\int \frac{7}{u} d u = 7 ln ∣ u ∣

= 5 u - 7 ln ∣ u ∣

Substitute back

u = t + 1

= 5 (t + 1) - 7 ln ∣ t + 1 ∣

Add a constant to the solution

= 5 (t + 1) - 7 ln ∣ t + 1 ∣ + C

\frac{d}{d x} (\frac{x}{12} + 1)

\int_{1}^{2} 2 x^{3} - 4 d x

\frac{\partial}{\partial x} (\frac{5 y ^{2}}{x})

\frac{2 s}{( s ^{2} + 4 ) ^{2}}

\frac{d}{d x} (\frac{x + 1}{x})

What is the integral of (5t-2)/(t+1) ?
The integral of (5t-2)/(t+1) is 5(t+1)-7ln|t+1|+C