Question

Integrate the following w.r.t.x. :-
$\sf{e^{5x} + x}$

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Answer 1

EXPLANATION.

⇒ ∫(e⁵ˣ + x)dx.

As we know that,

We can write equation individually, we get.

⇒ ∫(e⁵ˣ)dx + ∫(x)dx.

⇒ e⁵ˣ/5 + x²/2 + c.

                                                                                                                             

MORE INFORMATION.

Standard integrals.

(1) = ∫sin x dx = - cos x + c.

(2) = ∫cos x dx = sin x + c.

(3) = ∫tan x dx = ㏒(sec x ) + c = - ㏒(cos x ) + c.

(4) = ∫cot x dx = ㏒(sin x ) + c.

(5) = ∫sec x dx = ㏒(sec x + tan x) + c = - ㏒(sec x - tan x) + c = ㏒ tan(π/4 + x/2) + c.

(6) = ∫cosec x dx = - ㏒(cosec x + cot x) + c. = ㏒(cosec x - cot x) + c = ㏒ tan(x/2) + c.

(7) = ∫sec x tan x dx = sec x + c.

(8) = ∫cosec x cot x dx = - cosec x + c.

(9) = ∫sec²xdx = tan x + c.

(10) = ∫cosec²xdx = - cot x + c.

Answer 2

Answer:

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