Q100 / 150 · MHT CET 2017 · Mathematics

$\int \frac{\sec^{8} x}{cosec x} d x =$

A
$\frac{\sec^{8} x}{8} + c$
Correct answer
B
$\frac{\sec^{7} x}{7} + c$
C
$\frac{\sec^{6} x}{6} + c$
D
$\frac{\sec^{9} x}{9} + c$

Solution

I = \int \frac{\sec^{8} x}{cosec x} d x

Let

\cos x = t

- s i n x d x = d t

I = \int - \frac{d t}{t^{8}}

= \frac{1}{7} \frac{1}{t^{7}} + c

= \frac{\sec^{7} x}{7} + c

Hence, the correct answer is option: 'B'.

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