What is the integral of tarcsec(t) ?

The integral of tarcsec(t) is 1/2 t^2arcsec(t)-1/2 sqrt(t^2-1)+C

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integral of tarcsec(t)

\int t arcsec (t) d t

\frac{1}{2} t^{2} arcsec (t) - \frac{1}{2} t^{2} - 1 + C

Solution steps

\int t arcsec (t) d t

Apply Integration By Parts

= \frac{1}{2} t^{2} arcsec (t) - \int \frac{t ^{2}}{2 t ^{2} t ^{2} - 1} d t

\int \frac{t ^{2}}{2 t ^{2} t ^{2} - 1} d t = \frac{1}{2} t^{2} - 1

= \frac{1}{2} t^{2} arcsec (t) - \frac{1}{2} t^{2} - 1

Add a constant to the solution

= \frac{1}{2} t^{2} arcsec (t) - \frac{1}{2} t^{2} - 1 + C

s l o p e (3, - 3), (1, - 1)

t an g e n t f (x) = (1 + 2 x)^{11}, (0, 1)

\int sin (x) + sin (x) cos (x) d x

d er i v a t i v e (t + e^{t}) (3 - t)

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

What is the integral of tarcsec(t) ?
The integral of tarcsec(t) is 1/2 t^2arcsec(t)-1/2 sqrt(t^2-1)+C