\(\displaystyle \int_{0}^{\frac{\pi}{3}} 5 \tan^{5}(x) \sec^{4}(x) dx\)
\(\displaystyle \int_{0}^{\frac{\pi}{3}} 5[\tan^{5}(x))(\sec^{2}{x})(\sec^{2}(x))\)
\(\displaystyle \int_{0}^{\frac{\pi}{3}}5[\tan^{5}(x))(1 + tan^{2}(x))(\sec^{2}(x))\)
\(\displaystyle u = \tan x\)
\(\displaystyle du = \sec^{2}(x) dx\)
\(\displaystyle \int_{0}^{\frac{\pi}{3}} 5[(u^{5})(1 + u^{2})]\)
\(\displaystyle \dfrac{5u^{6}}{6} + \dfrac{u^{11}}{11}\) evaluated at \(\displaystyle [0,\dfrac{\pi}{3}\)
\(\displaystyle [\dfrac{5\tan^{6}(x)}{6} + \dfrac{\tan^{11}(x)}{11}]\)evaluated at \(\displaystyle [0,\dfrac{\pi}{3}]\)
\(\displaystyle [\dfrac{5\tan^{6}(\dfrac{\pi}{3})}{6} + \dfrac{\tan^{11}(\dfrac{\pi}{3})}{11}] - [\dfrac{5\tan^{6}(0)}{6} + \dfrac{\tan^{11}((0)}{11}] = 60.76257693\) ??
\(\displaystyle \int_{0}^{\frac{\pi}{3}} 5[\tan^{5}(x))(\sec^{2}{x})(\sec^{2}(x))\)
\(\displaystyle \int_{0}^{\frac{\pi}{3}}5[\tan^{5}(x))(1 + tan^{2}(x))(\sec^{2}(x))\)
\(\displaystyle u = \tan x\)
\(\displaystyle du = \sec^{2}(x) dx\)
\(\displaystyle \int_{0}^{\frac{\pi}{3}} 5[(u^{5})(1 + u^{2})]\)
\(\displaystyle \dfrac{5u^{6}}{6} + \dfrac{u^{11}}{11}\) evaluated at \(\displaystyle [0,\dfrac{\pi}{3}\)
\(\displaystyle [\dfrac{5\tan^{6}(x)}{6} + \dfrac{\tan^{11}(x)}{11}]\)evaluated at \(\displaystyle [0,\dfrac{\pi}{3}]\)
\(\displaystyle [\dfrac{5\tan^{6}(\dfrac{\pi}{3})}{6} + \dfrac{\tan^{11}(\dfrac{\pi}{3})}{11}] - [\dfrac{5\tan^{6}(0)}{6} + \dfrac{\tan^{11}((0)}{11}] = 60.76257693\) ??
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