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

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

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integral of (xtan(x))/(cos^2(x))

\int \frac{x tan ( x )}{cos ^{2} ( x )} d x

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

Solution steps

\int \frac{x tan ( x )}{cos ^{2} ( x )} d x

Rewrite using trig identities

= \int x sin (x) sec^{3} (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

\int \frac{1}{x ( x + 5 )} d x

\int sec (x) (5 sec (x) + 8 tan (x)) d x

\int 2 x^{3} + 3 x^{2} - 4 x + 5 d x

\int \frac{2 + x}{1 - x ^{2}} d x

\int x + \frac{3}{x} d x

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