Question

Solve the following

$\displaystyle\sf \int (x^e+e^x+e^e) dx$​

Answer 1

Step-by-step explanation:

We have,

$\int( {x}^{e} + {e}^{x} + {e}^{e} )dx$

$= \int{x}^{e} dx + \int {e}^{x}dx + \int {e}^{e} dx$

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

Answer 2

EXPLANATION.

$\sf \implies \int(x^{e} + e^{x} + e^{e} )dx.$

As we know that,

We can integrate individuals, we get.

$\sf \implies \int(x^{e} )dx + \int (e^{x} )dx + \int(e^{e} )dx$

As we know that,

⇒ ∫xⁿdx = xⁿ⁺¹/n + 1 + c.

$\sf \implies \dfrac{x^{e + 1} }{e + 1} + e^{x} + e^{e} .x + c.$

                                                                                                                       

MORE INFORMATION.

Standard integrals.

(1) = ∫0.dx = c.

(2) = ∫1.dx = x + c.

(3) = ∫k dx = kx + c, (k ∈ R).

(4) = ∫xⁿdx = xⁿ⁺¹/n + 1 + c, (n ≠ -1).

(5) = ∫dx/x = ㏒(x) + c.

(6) = ∫eˣdx = eˣ + c.

(7) = ∫aˣdx = aˣ/㏒(a) + c = aˣ ㏒(e) + c.