What is the integral from 0 to 1 of (1+12x)/(1+3x) ?

The integral from 0 to 1 of (1+12x)/(1+3x) is 4-2ln(2)

Popular >

integral from 0 to 1 of (1+12x)/(1+3x)

\int_{0}^{1} \frac{1 + 12 x}{1 + 3 x} d x

4 - 2 ln (2)

Decimal Notation

2.61370 \dots

Solution steps

\int_{0}^{1} \frac{1 + 12 x}{1 + 3 x} d x

Long division

\frac{1 + 12 x}{1 + 3 x} : 4 - \frac{3}{3 x + 1}

= \int_{0}^{1} 4 - \frac{3}{3 x + 1} d x

Apply the Sum Rule:

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

= \int_{0}^{1} 4 d x - \int_{0}^{1} \frac{3}{3 x + 1} d x

\int_{0}^{1} 4 d x = 4

\int_{0}^{1} \frac{3}{3 x + 1} d x = 2 ln (2)

= 4 - 2 ln (2)

\frac{\partial}{\partial x} (sin (2 x - y))

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

x \to 0 lim (e^{- 3 x})

\int \frac{27 arctan ( x )}{x ^{2}} d x

\frac{\partial}{\partial u} (\frac{u}{4 ( v - w ) ^{\frac{3}{2}}})

What is the integral from 0 to 1 of (1+12x)/(1+3x) ?
The integral from 0 to 1 of (1+12x)/(1+3x) is 4-2ln(2)