What is the integral of xtan(x)sec^2(x) ?

The integral of xtan(x)sec^2(x) is 1/2 xtan^2(x)-1/2 (-x+tan(x))+C

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integral of xtan(x)sec^2(x)

\int x tan (x) sec^{2} (x) d x

\frac{1}{2} x tan^{2} (x) - \frac{1}{2} (- x + tan (x)) + C

Solution steps

\int x tan (x) sec^{2} (x) d x

Apply Integration By Parts

: \frac{1}{2} x tan^{2} (x) - \int \frac{1}{2} tan^{2} (x) d x

= \frac{1}{2} x tan^{2} (x) - \int \frac{1}{2} tan^{2} (x) d x

\int \frac{1}{2} tan^{2} (x) d x = \frac{1}{2} (- x + tan (x))

= \frac{1}{2} x tan^{2} (x) - \frac{1}{2} (- x + tan (x))

Add a constant to the solution

= \frac{1}{2} x tan^{2} (x) - \frac{1}{2} (- x + tan (x)) + C

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What is the integral of xtan(x)sec^2(x) ?
The integral of xtan(x)sec^2(x) is 1/2 xtan^2(x)-1/2 (-x+tan(x))+C