Question

Verify the following reduction formula: 
\displaystyle \int \sec^n(u)\, du=\frac{\sec^{n-2}(u)\tan(u)}{n-1}+\frac{n-2}{n-1}\int \sec^{n-2}(u)\, du, \; n\neq 1∫secn(u)du=n−1secn−2(u)tan(u)​+n−1n−2​∫secn−2(u)du,n=1






koi mera friend banega? ​

Answer 1

.

Integrating Powers of Secants and Tangents

In many applications, particularly those involving arc length and surface area, one needs to evaluate integrals of the general form ∫tanmxsecnxdx, where m and n are positive integers. In the previous concept on integrating powers of sines and cosines, some useful integration rules were given based the identity sin2x+cos2x=1, the derivative relationships between the sine and cosine functions, and application of simple u-substitution or integration by parts techniques. In a similar way, useful guidelines for integrating powers of secants and tangents are derived by using their identity and derivative relationships. Before proceeding, see if you can write down the identity relationship between the tangent and secant functions (can you derive it using the sine/cosine relationship?). Do you know their derivative relationships? Can you evaluate ∫tanxsec2xdx?

Explanation:

ha mei tumari friend banungi