"Evaluate the indefinite integral. ∫dx(x+5)3" was answered by our experts

tugmiddelc0

Answered question

2021-11-06

Evaluate the indefinite integral.

\int \frac{d x}{{(x + 5)}^{3}}

Maked1954

Beginner2021-11-07Added 17 answers

Step 1
Evaluating :

\int \frac{d x}{{(x + 5)}^{3}}

Solution:
Using Substitution rule:
Let:
(x+5)=u
dx=du
Step 2
Substituting in the indefinite Integral:

\int \frac{d x}{{(x + 5)}^{3}} = \int \frac{d u}{u^{3}} = \int u^{- 3} d u

Applying the power rule of Integration:

\int u^{- 3} d u = \frac{u^{- 3 + 1}}{- 3 + 1} = \frac{u^{- 2}}{- 2} = - \frac{1}{2 u^{2}}

\int u^{- 3} d u = - \frac{1}{2 u^{2}} + C

Step 3
Substituting the value of u -back:
We get :

\int \frac{d x}{{(x + 5)}^{3}} = - \frac{1}{2 {(x + 5)}^{2}} + C

Hence,
This is the final answer.

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