Let nbsp;I=∫( 2t 4 ) nbsp;^ 4 dt Put 2t 4=u⇒ 2dt=du nbsp;∴ I=∫ 1 / 2 nbsp; u ^ 4 du= u ^ 3 / 6 +c nbsp;= 1 / 6( 2t 4 ) nbsp; ...

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Integration by Substitution

Solve ∫ 2t-...

Question

Solve $\int {(2 t - 4)}^{- 4} d t$

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Solution

Let $I = \int {(2 t - 4)}^{- 4} d t$
Put $2 t - 4 = u \Rightarrow 2 d t = d u$
$∴ I = \int \frac{1}{2} u^{- 4} d u = - \frac{u^{- 3}}{6} + c$
$= - \frac{1}{6 {(2 t - 4)}^{3}} + c$

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