Question

f 1÷x+3 dx
find the value chapter integration​

Answer 1

Step-by-step explanation:

Rewrite as  ∫   $x^{-3}$d x

and take the anti-derivative.

Explanation:

We first need to recognize that    $\frac{1}{x^{3} }$  is equivalent to   $x^{-3{$

Once we get that far, the problem becomes quite simple to solve.

Do be careful, however, as we are dealing with a negative exponent, so when we add one to the power as we take the anti-derivative, the magnitude of the power will decrease. This also means that our constant will have to be negative as well, since the x term in the integral is positive. Taking the anti-derivative, we get:

$-\frac{1}{2}$ · $x^{-2}$ + C

This is equivalent to

 

$-\frac{1}{2x^{2} } + C$

As usual, you can check this answer by taking the derivative, which gives you  $x^{-3}$