Please can it be proven by another means that ∫tan^2 xdx=tanx+x +c


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Question Number 29384 by NECx last updated on 08/Feb/18

$P l e a s e c a n i t b e p r o v e n b y a n o t h e r$ $m e a n s t h a t$ $\int \tan^{2} x d x = t a n x + x + c$
Commented by abdo imad last updated on 08/Feb/18

$l e t p u t I = \int {t a n}^{2} x d x t h e c h . t a n x = t g i v e$ $I = \int t^{2} \frac{d t}{1 + t^{2}} = \int \frac{1 + t^{2} - 1}{1 + t^{2}} d t = t - \int \frac{d t}{1 + t^{2}} \Rightarrow$ $I = t - a r c t a n t + λ = t a n x - x + λ .$
Commented by abdo imad last updated on 08/Feb/18

$t h e r e i s a e r r o r i n t b e q u e s t i o n!$
Commented by NECx last updated on 08/Feb/18

$w o w . . . . T h a n k s$
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