Question

integration for x power -5+x power-7+2​

Answer 1

Answer:

$\displaystyle \longrightarrow2x-\frac{1}{4x^{4}} -\frac{1}{6x^{6}} +C$

Step-by-step explanation:

Let :

$\displaystyle \text{I}=\int\limits{(x^{-5}+x^{-7}+2}) \, dx$

$\displaystyle \longrightarrow \text{I}=\int\limits{x^{-5}} \ dx+\int\limits{x^{-7}} \ dx+\int\limits{2} \, dx$

We have formula :

$\displaystyle \int\limits{x^n} \, dx =\frac{x^{n+1}}{n+1} +C$

$\displaystyle \longrightarrow \text{I}=\frac{x^{-5+1}}{-5+1} +\frac{x^{-7+1}}{-7+1} +2x+C$

$\displaystyle \longrightarrow \text{I}=\frac{x^{-4}}{-4} +\frac{x^{-6}}{-6} +2x+C$

$\displaystyle \longrightarrow \text{I}=-\frac{x^{-4}}{4} -\frac{x^{-6}}{6} +2x+C$

$\displaystyle \longrightarrow \text{I}=2x-\frac{1}{4x^{4}} -\frac{1}{6x^{6}} +C$

Hence we get required answer!

Answer 2

Answer:

$\displaystyle \longrightarrow2x-\frac{1}{4x^{4}} -\frac{1}{6x^{6}} +C$

Step-by-step explanation:

Let :

$\displaystyle \text{I}=\int\limits{(x^{-5}+x^{-7}+2}) \, dx$

$\displaystyle \longrightarrow \text{I}=\int\limits{x^{-5}} \ dx+\int\limits{x^{-7}} \ dx+\int\limits{2} \, dx$

We have formula :

$\displaystyle \int\limits{x^n} \, dx =\frac{x^{n+1}}{n+1} +C$

$\displaystyle \longrightarrow \text{I}=\frac{x^{-5+1}}{-5+1} +\frac{x^{-7+1}}{-7+1} +2x+C$

$\displaystyle \longrightarrow \text{I}=\frac{x^{-4}}{-4} +\frac{x^{-6}}{-6} +2x+C$

$\displaystyle \longrightarrow \text{I}=-\frac{x^{-4}}{4} -\frac{x^{-6}}{6} +2x+C$

$\displaystyle \longrightarrow \text{I}=2x-\frac{1}{4x^{4}} -\frac{1}{6x^{6}} +C$

And We Got The Required Answer.