Integrate the function in Exercise: x ^2x - Vidyadip

Question

Integrate the function in Exercise:
$\text{x} \ \sec^2\text{x}$

✓

Answer

Let $\text{I}=\int\text{x}\sec^2\text{x dx}$
Taking x as first function and sec²x as second function and integrating by parts, we obtain.
$\text{I}=\text{x}\int\sec^2\text{x dx}-\int\Big[\Big\{\frac{\text{d}}{\text{dx}}\text{x}\int\sec^2\text{x} \ \text{dx}\Big\}\text{dx}\Big]$
$=\text{x}\tan\text{x}-\int1.\tan\text{x dx}$
$=\text{x}\tan\text{x}+\text{log}|\cos\text{x}|+\text{C}$

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