Let ${I_n} = \int {{{\tan }^n}x\,dx} ,\,\left( {n > 1} \right).$ If ${I_4} + {I_6}$ = $a{\tan ^5}x + b{x^5} + C$, where C is a constant of integration, then the ordered pair $\left( {a,b} \right)$ is equal to

Question

Let ${I_n} = \int {{{\tan }^n}x\,dx} ,\,\left( {n > 1} \right).$

If ${I_4} + {I_6}$ = $a{\tan ^5}x + b{x^5} + C$, where C is a constant of integration,

then the ordered pair $\left( {a,b} \right)$ is equal to

$\left( {{1 \over 5},0} \right)$

$\left( {{1 \over 5}, - 1} \right)$

$\left( { - {1 \over 5},0} \right)$

$\left( { - {1 \over 5},1} \right)$

Solution

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