Indefinite Integrals

Appeared 64 times across 16 years of JEE Main papers — about 4.0 questions a year. Every one of them is below, with a full worked solution.

Questions per year

2’04

1’05

1’07

1’08

1’12

1’13

1’15

3’16

3’17

4’18

16’19

9’20

5’21

4’22

6’23

6’24

01Medium64×since 2004Q4006

Let

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

{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