# Evaluate the following integrals:

=

Adding the powers : -4 + -2 = -6

Since all are even nos, we will divide each by cos⁶x to convert into positive power

So, =

=

= { since sec2x = 1 + tan2x}

= ( apply (a + b)2 = a2 + b2 + 2ab )

Let tanx = t, so dt = d(tanx) = sec2xdx

So,

Put t and dx in the above equation,

=

=

=

=

=

=

= {1/tanx = cotx)

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