Mathematics

$$\int {\dfrac{{2x + 7}}{{{{(x - 4)}^2}}}dx} $$


SOLUTION

We have,

$$I=\int{\dfrac{2x+7}{{{\left( x-4 \right)}^{2}}}dx}$$

 

Let $$t=x-4$$

$$dt=dx$$

 

Therefore,

$$ I=\int{\dfrac{2\left( t+4 \right)+7}{{{t}^{2}}}dt} $$

$$ I=\int{\dfrac{2t+8+7}{{{t}^{2}}}dt} $$

$$ I=\int{\dfrac{2t+15}{{{t}^{2}}}dt} $$

$$ I=\int{\dfrac{2t}{{{t}^{2}}}dt}+\int{\dfrac{15}{{{t}^{2}}}dt} $$

$$ I=\ln \left( {{t}^{2}} \right)-\dfrac{15}{t}+C $$

 

On putting the value of $$t$$, we get

$$I=\ln \left( {{\left( x-4 \right)}^{2}} \right)-\dfrac{15}{\left( x-4 \right)}+C$$

 

Hence, this is the answer.

View Full Answer

Its FREE, you're just one step away

Create your Digital Resume For FREE on your name's sub domain "yourname.wcard.io". Register Here!


Subjective Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 124
Enroll Now For FREE

Realted Questions

Q1 Single Correct Medium
The value of $$\displaystyle  \int_0^1 \sqrt{x} \cdot e^{\sqrt{x}} dx $$ is equal to 
  • A. $$ \dfrac {(e-2)}{2} $$
  • B. $$ 2e-1$$
  • C. $$ 2 (e-1) $$
  • D. $$ \dfrac {e-1}{2} $$
  • E. $$ 2 ( e-2) $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Medium
$$\int _{ 2 }^{ 4 }{ \frac { x }{ { x }^{ 2 }+1 }  } dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Medium
Evaluate the following integral as the limit of sum:
$$\displaystyle\int^2_0(x+4)dx$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Subjective Hard
Evaluate: $$\displaystyle \int { \dfrac { { x }^{ 2 } }{ 1+{ x }^{ 4 } }  } dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Easy
$$\int(2x^2-3 \, sin x+5 \sqrt{x})dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer