Oct
2012

# What is the integral of tangent squared

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$\sec^2x-1=\tan^2x$ $\displaystyle\int{\tan^2x}\,dx=\displaystyle\ int{\sec^2x-1}\,dx$ Using the Sum Rule: [math]\displaystyle\int{\sec^2x-1}\. Explanation: We will use the Trigo. Identity:sec2x=tan2x+1. Hence, ∫(tanx)2dx= ∫tan2xdx=∫(sec2x−1)dx. =∫sec2xdx−∫1dx=tanx−x+C. You can start by writing tan2(x)=sin2(x)cos2(x) giving: ∫tan2(x)dx=∫sin2(x)cos2 (x)dx= using: sin2(x)=1−cos2(x) you get.

Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. Type in any integral Use the following identity: sec 2(x)−tan 2(x)=1 . (integral) xn dx = x(n+1) / (n+1) + C (n -1) Proof, (integral) 1/x dx = ln|x| + C ( integral) tan x dx = -ln|COs x| + C Proof, (integral) cot x dx = ln|sin x| + C Proof. This is a question which tests your knowledge of how to use trigonometric identities as well as integration. As there is no way to immediately integrate tan^2 (x).

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