# How do you evaluate \int 5( 4- 3x ) ^ { 6} d x?

Feb 6, 2018

$\setminus m b \otimes \left\{T h e a n s w e r i s\right. \setminus q \quad - \frac{5}{21} {\left(4 - 3 x\right)}^{7} + C$

#### Explanation:

$\setminus$

$\setminus m b \otimes \left\{T h i s c a n b e a \chi e v e d b y a s i m p \le \subset s t i t u t i o n\right\} \setminus \setminus \setminus m b \otimes \left\{\left[\mathmr{and} e v e n b y s i g h t , \mathmr{if} y o u c a n s e e i t\right] .\right\}$

$\setminus m b \otimes \left\{S u b s t i t u t i o n\right. \setminus q \quad u = 4 - 3 x$

$\setminus m b \otimes \left\{T h u s\right. \setminus q \quad \mathrm{du} = - 3 \mathrm{dx}$

$\setminus m b \otimes \left\{S o l v \in g f \mathmr{and}\right\} \setminus \mathrm{dx} : \setminus q \quad \mathrm{dx} = - \frac{\mathrm{du}}{3}$

$\setminus m b \otimes \left\{H e n c e , t h e \int\right. \setminus q \quad \setminus \int 5 {\left(4 - 3 x\right)}^{6} \mathrm{dx} = \setminus \int 5 {u}^{6} \left(- \frac{\mathrm{du}}{3}\right) = - \frac{5}{3} \setminus \int {u}^{6} \mathrm{du} = - \frac{5}{3} {u}^{7} / 7 = - \frac{5}{21} {\left(4 - 3 x\right)}^{7} + C$