Evaluate the integral $$ \int \frac{d x}{(2 x+2)^{4}}, $$ by making the appropriate substitution: $$ u=\square $$

Question

Hall Norton · Accepted Answer

To evaluate the integral $$ \int \frac{d x}{(2 x+2)^{4}} $$, substitute $$ u = 2x + 2 $$ and $$ du = 2dx $$. The integral becomes $$ \frac{1}{2} \int u^{-4} du $$, which simplifies to $$ -\frac{1}{6u^3} + C $$ or $$ -\frac{1}{6(2x + 2)^3} + C $$.

Evaluate the integral \[ \int \frac{d x}{(2 x+2)^{4}}, \] by making the appropriate substitution: \( u=\square \)

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Evaluate the integral \[ \int \frac{d x}{(2 x+2)^{4}}, \] by making the appropriate substitution: \( u=\square \)

Solución ThothAI de Upstudy

Respuesta rápida

Solución paso a paso

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