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sec-5-3x-sec3xtan-3xdx-




Question Number 83276 by 09658867628 last updated on 29/Feb/20
∫sec^5 3x•sec3xtan 3xdx
$$\int\mathrm{s}{ec}^{\mathrm{5}} \mathrm{3}{x}\bullet\mathrm{s}{ec}\mathrm{3}{x}\mathrm{tan}\:\mathrm{3}{xdx} \\ $$
Answered by TANMAY PANACEA last updated on 29/Feb/20
t=sec3x→dt=3sec3x.tan3x dx  ∫t^5 ×(dt/3)=(t^6 /(18))+c  (((sec3x)^6 )/(18))+c
$${t}={sec}\mathrm{3}{x}\rightarrow{dt}=\mathrm{3}{sec}\mathrm{3}{x}.{tan}\mathrm{3}{x}\:{dx} \\ $$$$\int{t}^{\mathrm{5}} ×\frac{{dt}}{\mathrm{3}}=\frac{{t}^{\mathrm{6}} }{\mathrm{18}}+{c} \\ $$$$\frac{\left({sec}\mathrm{3}{x}\right)^{\mathrm{6}} }{\mathrm{18}}+{c} \\ $$

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