The integral is given as, I= #x222B; x sec 2 xdx Use integration by parts. Consider sec ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Integration by Parts

12. x 2 x

Question

12. x sec2x

Open in App

Solution

The integral is given as,

I= ∫ x sec 2 xdx

Use integration by parts. Consider sec 2 x as second function and x as the first function.

I= ∫ x sec 2 xdx =x ∫ sec 2 xdx − ∫ ( d dx x ∫ sec 2 xdx )dx =xtanx− ∫ tanxdx I=xtanx+log| cosx |+C

Thus, the integration of ∫ x sec 2 xdx is xtanx+log| cosx |+C.

Suggest Corrections

Similar questions

{log}_{1 / 4} (\frac{35 - x^{2}}{x}) \geq - \frac{1}{2}

L i m x \to 0 \frac{sec x - 1}{x^{2} (sec x + 1)^{2}} =

f (x) = {\begin{matrix} (x - 1)^{2} + 4 x < 1 a + x^{2} x \geq 1 \end{matrix}

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

\cos^{- 1} (4 x^{3} - 3 x)

\tan^{- 1} (\frac{\sqrt{1 - x^{2}}}{x}), if \frac{1}{2} < x < 1

Join BYJU'S Learning Program