$\smallint \,\,\frac{{({{\sec }^2}\,\,x\,\, - \,\,7)}}{{{{\sin }^7}\,\,x}}\,\,\;dx$is equal to

$\frac{{\cos \,\,x}}{{{{\sin }^7}\,\,x}}\,\, + \,\,c$

$\frac{{\sin \,\,x}}{{{{\cos }^7}\,\,x}}\,\, + \,\,c$

$\frac{{\sin \,\,x}}{{{{\tan }^7}\,\,x}}\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Medium

1 of 1

Application +4 | -1

\int \,\,\frac{{({{\sec }^2}\,\,x\,\, - \,\,7)}}{{{{\sin }^7}\,\,x}}\,\,\;dx

is equal to

View answer and explanation

Correct option: A

\frac{{\tan \,\,x}}{{{{\sin }^7}\,\,x}}\,\, + \,\,c

Option A is correct because the given integral simplifies to the derivative of (tan x) / (sin⁷ x), making the solution (tan x) / (sin⁷ x) + c.