∫ sec 8 ⁡ x cosec ⁡ x d x =, sec 8 ⁡ x 8 + c, sec 7 ⁡ x 7 + c, sec 6 ⁡ x 6 + c, sec 9 ⁡ x 9 + c

I = ∫ sec 8 x cosec x d x Let cos ⁡ x = t - s i n x d x = d t I = ∫ - d t t 8 = 1 7 1 t 7 + c = sec 7 ⁡ x 7 + c

∫ sec 8 ⁡ x cosec ⁡ x d x =

Question: Answered & Verified by Expert

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

MathematicsIndefinite IntegrationJEE Main

Options:

Solution:

2532 Upvotes Verified Answer

The correct answer is:

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

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

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