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

The integral of xtan^2(x) is -x^2+xtan(x)+(x^2)/2+ln|cos(x)|+C

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integral of xtan^2(x)

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

- x^{2} + x tan (x) + \frac{x ^{2}}{2} + ln ∣ cos (x) ∣ + C

Solution steps

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

Apply Integration By Parts

: x (- x + tan (x)) - \int - x + tan (x) d x

= x (- x + tan (x)) - \int - x + tan (x) d x

\int - x + tan (x) d x = - \frac{x ^{2}}{2} - ln ∣ cos (x) ∣

= x (- x + tan (x)) - (- \frac{x ^{2}}{2} - ln ∣ cos (x) ∣)

Simplify

x (- x + tan (x)) - (- \frac{x ^{2}}{2} - ln ∣ cos (x) ∣) : - x^{2} + x tan (x) + \frac{x ^{2}}{2} + ln ∣ cos (x) ∣

= - x^{2} + x tan (x) + \frac{x ^{2}}{2} + ln ∣ cos (x) ∣

Add a constant to the solution

= - x^{2} + x tan (x) + \frac{x ^{2}}{2} + ln ∣ cos (x) ∣ + C

\frac{d}{d x} (5 sin (x) + 2 cos (x))

f (x) = e^{x + 1} + 7

\int - \frac{3}{2} e^{- x} sin (2 x) d x

\int - \frac{2 x ^{2}}{5} + \frac{3 x}{4} - \frac{1}{6} d x

\frac{d}{d x} (e^{- \frac{x ^{2}}{2}})

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