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Question Number 14181 by tawa tawa last updated on 29/May/17

$$\int {\sec }^6\left(\mathrm{x}\right)\mathrm{dx}$$

Answered by ajfour last updated on 29/May/17

$$let\tan x=t$$$$\Rightarrow \sec {}^{2}xdx=dt,andweknow$$$$1+\tan {}^{2}x=\sec {}^{2}x$$$$\int \left(\sec {}^{4}x\right)\sec {}^{2}xdx=\int {(1+t^2)}^{2}dt$$$$=\int (1+2t^2+t^4)dx$$$$=t+\frac{2}{3}{t}^3+\frac{t^5}{5}+C.$$$$\left(replace\tan xfor\mathit{t}\right).$$

Commented by tawa tawa last updated on 29/May/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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