What is the integral of xtan(x)tan(x) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of xtan(x)tan(x)

\int x tan (x) tan (x) d x

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

Solution steps

\int x tan (x) tan (x) d x

Simplify

x tan (x) tan (x) : x tan^{2} (x)

= \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

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

\int 14 sin (x) - 5 cos (x) d x

\int \frac{x}{2 x ^{2} - 4 x - 7} d x

\int \frac{x + 1}{x + 9} d x

\int 2 x^{3} + 2 d x

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