Mathematics: How do we solve this?

How do we solve this? - id14078118, chutchins0406

jcblake

12.08.2021

$-\frac{1}{36\left(6x+1\right)^6} +C$

Step-by-step explanation:

we're going to us u substitution

$\int (6x+1)^-7 dx$

u=6x+1

$\int\frac{1}{6u^7} du$

take out the constant, $\frac{1}{6}$

$\frac{1}{6}$ · $\int u^-7du$

next use the power rule, $\int x^adx=\frac{x^{a+1}}{a+1},\:\quad \:a\ne -1$

$\frac{1}{6}\cdot \frac{u^{-7+1}}{-7+1}$

simplify by substituting 6x+1 for

$\frac{1}{6}\cdot \frac{(6x+1)^{-7+1}}{-7+1} = -\frac{1}{36\left(6x+1\right)^6}$

add a constant,

$-\frac{1}{36\left(6x+1\right)^6} +C$

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