Mathematics

Evaluate: $$\int x \sec ^ { 2 } x d x$$


SOLUTION
$$I=\int x\sec^2xdx$$

We know that
$$\int uv =u\int v-\int (\int v)\dfrac{du}{dx}.dx$$

$$u=x$$   $$v=\sec ^2x$$

$$I=x\int \sec ^2x-\int (\int \sec ^2x).1dx$$

$$I=x\tan x-\int \tan xdx$$

$$I=x\tan x-\ln |\sec x|+c$$.
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Subjective Medium Published on 17th 09, 2020
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