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

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

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integral of x(tan(x))^2

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

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

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

Add a constant to the solution

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

x^{2} + 1, 3 - x, x = 0

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n = 1 \sum \infty n ln (2)

\int sin^{2} (v) cos^{3} (v) d v

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