What is the integral of 1/((x+3)^4) ?

The integral of 1/((x+3)^4) is -1/(3(x+3)^3)+C

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integral of 1/((x+3)^4)

\int \frac{1}{( x + 3 ) ^{4}} d x

- \frac{1}{3 ( x + 3 ) ^{3}} + C

Solution steps

\int \frac{1}{( x + 3 ) ^{4}} d x

Apply u-substitution

= \int \frac{1}{u ^{4}} d u

Apply the Power Rule

= - \frac{1}{3 u ^{3}}

Substitute back

u = x + 3

= - \frac{1}{3 ( x + 3 ) ^{3}}

Add a constant to the solution

= - \frac{1}{3 ( x + 3 ) ^{3}} + C

What is the integral of 1/((x+3)^4) ?
The integral of 1/((x+3)^4) is -1/(3(x+3)^3)+C