Mathematics

$$\int { \cfrac { \left( { x }^{ 3 }+3 \right) \left( x-2\right)  }{ \left( { x }^{ 2 }-4x+4 \right)  }  }dx$$


SOLUTION
We have,
$$I=\int { \cfrac { \left( { x }^{ 3 }+3 \right) \left( x-2\right)  }{ \left( { x }^{ 2 }-4x+4 \right)  }  }dx$$

$$I=\int { \cfrac { \left( { x }^{ 3 }+3 \right) \left( x-2\right)  }{ \left( x-2 \right)^2  }  }dx$$

$$I=\int { \cfrac { \left( { x }^{ 3 }+3 \right)  }{ \left( x-2 \right)  }  }dx$$

$$I=\int \left(x^2+2x+4+\cfrac{11}{x-2}\right)dx$$

$$I=\dfrac{x^3}{3}+2\dfrac{x^2}{2}+4x+11\ln (x-2)+C$$

$$I=\dfrac{x^3}{3}+x^2+4x+11\ln (x-2)+C$$

Hence, this is the answer.
View Full Answer

Its FREE, you're just one step away


Subjective Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86
Enroll Now For FREE

Realted Questions

Q1 Subjective Hard
Evaluate the given integral.
$$\displaystyle \int { \tan ^{ -1 }{ \left( \cfrac { 2x }{ 1-{ x }^{ 2 } }  \right)  }  } dx\quad $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Medium
Evaluate $$\int { \sin ^{ 3 }{ x } \cos ^{ 2 }{ x } dx } $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Medium
$$\displaystyle\int {\dfrac{{{{\tan }^4}\sqrt x \,{{\sec }^2}\sqrt x }}{{\sqrt x }}} \,dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Hard
If $$\displaystyle{\int \frac{\displaystyle dx}{\displaystyle \sqrt{x}+\displaystyle \sqrt[3]{x}}}=a\sqrt{x}+b(\sqrt[3]{x})+c(\sqrt[6]{x})+d\: \ln(\sqrt[6]{x}+1)+e$$, $$e$$ being arbitrary constant then. Find the value of $$20a + b + c + d.$$
  • A. $$35$$
  • B. $$43$$
  • C. $$47$$
  • D. $$37$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Medium
Find the value $$\displaystyle\int\limits_{-\dfrac{\pi}{2}}^{\dfrac{\pi}{2}} \sin^{2017}x\cos ^{2018}x\ dx$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer