Question

integral 1/x^3dx how??

Answer 1

$\int \frac{1}{ {x}^{3} } dx \\ = \int {x}^{ - 3} dx$
we know,
$\int\:x^ndx=\frac{x^{n+1}}{n+1}+C$

$so, =\int \: x^{-3}dx=\frac{x^{-3+1}}{-3+1}\\=\frac{x^{-2}}{-2}\\=\frac{ - 1}{2x^2} + C$

Answer 2

Given  ∫ 1/x^3 dx

Use the power rule i.e  ∫ x^n dx = n^(n+1) / (n+1)  + C

∫ 1 / x^3 dx

= - 1 / (2x^2) + C