Find the integral of the given function w-r-t - x y - e 2 x -1- x 2A- 2-e2 x-1-x-cB- e2 x-2x-1-x-cC- e2 x-2-1-x-cD- e2 x-1-x-c

The correct option is C y=e^2x+1/x^2 Integration both side w.r.t. 'x', I=∫ y.dx=∫ e^2x+1/x^2 dx=e^2x/2+x^ 2+1/ 2+1+c [ ∵∫ e^ax=e^ax/a+c ] I=e^2x/2 1/x+c ...

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

Byju's Answer

Standard XII

Physics

Antiderivative

Find the inte...

Question

Find the integral of the given function w.r.t - x

$y = e^{2 x} + \frac{1}{x^{2}}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C

$y = e^{2 x} + \frac{1}{x^{2}}$

Integration both side w.r.t. 'x',

$I = \int y . d x = \int ⟮ e^{2 x} + \frac{1}{x^{2}} ⟯ d x = \frac{e^{2 x}}{2} + \frac{x^{- 2 + 1}}{- 2 + 1} + c [∵ \int e^{a x} = \frac{e^{a x}}{a} + c]$

$I = \frac{e^{2 x}}{2} - \frac{1}{x} + c$

Suggest Corrections

Similar questions

Let I $= \int \frac{e^{x}}{e^{4 x} + e^{2 x} + 1} d x . J = \int \frac{e^{- x}}{e^{- 4 x} + e^{- 2 x} + 1} d x,$ Then, for an arbitrary constant c, the value of J-I equals

Q. Differentiate

y = [\frac{e^{2 x} + e^{- 2 x}}{e^{2 x} - e^{- 2 x}}]

w.r.t

x

Q. Integrate the following w.r.t.

x

e^{2 x} + \frac{1}{x^{2}}

$\int e^{2 x}$ [sec 2x + sec 2x.tan 2x]dx

Q. Integrate the function

\frac{e^{2 x} - 1}{e^{2 x} + 1}

Join BYJU'S Learning Program

Find the integral of the given function w.r.t - x y=e2x+1x2

The correct option is C y=e2x+1x2 Integration both side w.r.t. 'x', I=∫y.dx=∫⟮e2x+1x2⟯dx=e2x2+x−2+1−2+1+c[∵∫eax=eaxa+c] I=e2x2−1x+c

Find the integral of the given function w.r.t - x

$y = e^{2 x} + \frac{1}{x^{2}}$

The correct option is C

$y = e^{2 x} + \frac{1}{x^{2}}$

Integration both side w.r.t. 'x',

$I = \int y . d x = \int ⟮ e^{2 x} + \frac{1}{x^{2}} ⟯ d x = \frac{e^{2 x}}{2} + \frac{x^{- 2 + 1}}{- 2 + 1} + c [∵ \int e^{a x} = \frac{e^{a x}}{a} + c]$

$I = \frac{e^{2 x}}{2} - \frac{1}{x} + c$