Let `I_n=inttan^n xdx ,(n >1)` If `I_4+I_6=atan^5x+b x^5+C ,` Where `C` is a constant of integration, then the ordered pair `(a , b)` is equal to : (1) `(5/1,-1)` (2) `(-1/(5,0))` (3) `(-1/5,1)` (4) `(1/5,0)`

Options

A. `(-(1)/(5),0)`
B. `(-(1)/(5),1)`
C. `((1)/(5),0)`
D. `((1)/(5),-1)`

Explanation

To solve the problem, we need to find the ordered pair \((a, b)\) such that \(I_4 + I_6 = a \tan^5 x + b x^5 + C\), where \(C\) is a constant of integration.

### Step-by-Step Solution:

1. **Define the Integrals**:
We start with the definitions:
\[
I_n = \int \tan^n x \, dx
...