The indefinite integral (I) for [tex]\int_{}^{}x^{4}dx[/tex] = 33e²/³ˣ + C
A function that takes the antiderivative of another function is known as an indefinite integral. It is represented graphically as an integral symbol, a function, and finally a dx.
Lets start by making "I₁" = [tex]\int_{}^{}x^{4}dx[/tex]
Because we already determined that [tex]\int_{}^{}x^{n}dx[/tex] = [(Xⁿ⁺¹)/(n+1)] + C, nt Integer
⇒ I₁ = [tex]\int_{}^{}x^{4}dx[/tex] = [(X⁴⁺¹)/(4+1)] + C,
= x⁵/5 + C
Let us make 'I'₁ = [tex]\int_{}^{}e^{2/3x}dx[/tex] [If we make 2/3x = t
I₂ ⇒
I₂ = 22[tex]\int_{}^{}e^{2/3x}dx[/tex]
= 33 [tex]\int_{}^{}e^{t}dt[/tex]
I₂ = 33e^t + C
⇒ I₂ = 33e²/³ˣ + C
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