Question

How do we solve this?

Answer 1

Answer:

$= - \frac{1}{36(6x + 1) ^{6} } + c$

I hope I helped you^_^

Answer 2

Answer:

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

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 $u$

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

add a constant, $C$

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