Mathematics

$$\displaystyle \int { \frac { \cos { x } +x\sin { x }  }{ x\left( x+\cos { x }  \right)  } dx } $$ is equal to 


ANSWER

$$\displaystyle \log { \left| \frac { x }{ x+\cos { x } } \right| +c } $$


SOLUTION
$$\displaystyle \int { \frac { \cos { x } +x\sin { x }  }{ x\left( x+\cos { x }  \right)  } dx } =\int { \frac { \left( x+\cos { x }  \right) -x\left( 1-\sin { x }  \right)  }{ x\left( x+\cos { x }  \right)  } dx } $$

$$\displaystyle =\int { \left( \frac { 1 }{ x } -\frac { 1-\sin { x }  }{ x+\cos { x }  }  \right) dx } =\log { \left| x \right|  } -\log { \left| x+\cos { x }  \right|  } +c$$

$$\displaystyle =\log { \left| \frac { x }{ x+\cos { x }  }  \right| +c } $$
View Full Answer

Its FREE, you're just one step away


Single Correct Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 114
Enroll Now For FREE

Realted Questions

Q1 Subjective Medium
Integrate : $$\displaystyle \int e^x \cdot \frac {x}{(1+x)^2}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Medium
Integrate $$\int {({{\sin }^{ - 1}}} x{)^2}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Hard
If $$ \displaystyle I_1=\int_{0}^{\frac{\pi}{2}}e^{-x} sin  4x  dx$$  and $$ \displaystyle I_2=\int_0^{2\pi}e^{-x} sin  4x  dx$$ and  $$ \displaystyle I_2=\lambda I_1$$, then $$ \displaystyle \lambda$$ is equal to
  • A. $$\displaystyle \frac{e^{2\pi}-1}{e^{\pi}-1}$$
  • B. $$\displaystyle \frac{e^{\pi}-1}{1-e^{2\pi}}$$
  • C. $$ \displaystyle \frac{1-e^{2\pi}}{1-e^{\frac{\pi}{2}}}$$
  • D. $$ \displaystyle \frac{1-e^{-2\pi}}{1-e^{-\frac{\pi}{2}}}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Subjective Medium

Evaluate the following definite integral:

$$\displaystyle\int_{0}^{\pi/4}\sin^{3}2t\cos 2t\ dt$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Medium
Evaluate:
$$\displaystyle\int\limits_{-a}^{a}x^3\sqrt{x^2-a^2}\ dx$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer