Question

evaluate the integral (7-3x)⁴
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Answer 1

$\implies \int (7-3x)^{4} dx$

$\text{Let }7-3x = t$

$\implies dt = -3dx$

$\implies -\dfrac{dt}{3} = dx$

$\text{Substituting in the integral}$

$\implies \int t^{4} \huge{\text{(}}-\dfrac{dt}{3}\huge{\text{)}}$

$\implies -\dfrac13\int t^{4}dt$

$\implies -\dfrac13\times \dfrac{t^{5}}{5} + C$

$\implies \dfrac{-t^{5}}{15} + C$

$\implies \dfrac{-(7-3x)^{5}}{15} + C$

$\implies \boxed{\dfrac{(3x-7)^{5}}{15} + C}$