Calc1.53

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\int \tan x\sec ^{2}x\,dx\,

If you'll notice, the derivative of \tan x\, is \sec ^{2}x\, which we already have.

u=\tan x\,

du=\sec ^{2}xdx\,

Plugging these into the integral gives

\int \tan x\sec ^{2}x\,dx=\int u\,du={\frac  {1}{2}}u^{2}+C={\frac  {1}{2}}\tan ^{2}x+C\,


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