What is the integral of x*tan^2(x) ?

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

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integral of x*tan^2(x)

\int x \cdot 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

x \to 0 lim (3 x + 1)

\frac{y ^{^{'}} - e ^{- t} + 3}{y} = - 3

n \to \infty lim (i = 1 \sum n (1 + \frac{2 i}{n})^{3} (\frac{2}{n}))

\frac{d}{d x} (\frac{x ^{3} + x - 2}{x - x ^{2}})

\frac{d}{d x} (e^{(1 - x^{2} - \frac{y ^{2}}{4})})

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