integrate tan^{2}x

Haven

Haven

Answered question

2021-01-27

integrate tan2x

Answer & Explanation

Lacey-May Snyder

Lacey-May Snyder

Skilled2021-01-28Added 88 answers

tan2x dx =sin2x{cos2}x dx =1(cos2x}{cos2x} dx =1cos2x1 dx   
From here, we are essentially going to use the properties of the integral and the fundamental theorem of calculus. Notice that (tanx)(d/dx)=1/(cos2)x, so by the fundamental theorem of calculus, 1/(cos2)xdx=tanx
Thus: 
1cos2x1 dx =1cos2x dx  dx =tanxx+c

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