Question

usando o metodo de integração por substituição determine a integral f (2x - 1)5 2dx
a) ( 2X-1)6 +C /3
b) (2x -1)5 +c /5
c) (2x-1)6 +c /6
d) 10.(2x-1)4 +c

Answer 1

$\int(2x-1)^{5}2dx$

Chamemos 2x - 1 de u:

$u=2x-1$

Derivando u:

$\dfrac{du}{dx}=1\cdot2x^{1-1}-0\\\\\\\dfrac{du}{dx}=2\\\\\\\boxed{du=2dx}$
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Então, temos que:

$\int(2x-1)^{5}2dx=\int u^{5}du\\\\\\\int(2x-1)^{5}2dx=\dfrac{u^{5+1}}{5+1}+C\\\\\\\int(2x-1)^{5}2dx=\dfrac{u^{6}}{6}+C$

Como u = 2x - 1:

$\boxed{\boxed{\int(2x-1)^{5}2dx=\dfrac{(2x-1)^{6}}{6}+C}}$