Mathematics

$$\displaystyle \int \dfrac{1}{(x + 1)\sqrt{x + 2}}dx =$$


SOLUTION
Let, $$I=$$$$\displaystyle \int \dfrac{1}{(x + 1)\sqrt{x + 2}}dx $$
Put $$x+2=z^2$$ then $$dx=2z\ dz$$.
Using these in the above integration we get,
$$I=$$$$\displaystyle \int \dfrac{2z\ dz}{(z^2 - 1)z}dx $$
or, $$I=$$$$2\displaystyle \int \dfrac{ dz}{(z^2 - 1)}dx $$
or, $$I=$$$$2.\dfrac{1}{2.1}\log\left|\dfrac{z-1}{z+1}\right|+c $$ [ Where $$c$$ integrating constant]
or, $$I=$$$$\log\left|\dfrac{\sqrt{x+2}-1}{\sqrt{x+2}+1}\right|+c $$
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 Medium
Write a value of 
$$\int { \sqrt { { x }^{ 2 }-9 }  } \  dx\quad $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Hard
Integrate the function    $$\cfrac {x+3}{x^2-2x-5}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Medium
Evaluate:$$\displaystyle\int{\tan{x}\tan{2x}dx}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Multiple Correct Medium
$$\displaystyle \int 2^{mx}.3^{nx}dx$$ when $$m,n\epsilon N$$ is equal to:
  • A. $$\displaystyle \frac{2^{mx}+3^{nx}}{m \ln 2+n\ln 3}+c$$
  • B. None of these
  • C. $$\displaystyle\frac{e^{(mx\ln2+nx\ln3)}}{m\ln2+n\ln3}+c$$
  • D. $$\displaystyle\frac{2^{mx}.3^{nx}}{\ln(2^{m}\cdot 3^{n})}+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Medium
Solve: $$\int\limits_0^{\frac{\pi }{2}} {{{\sin }^2}x{{\cos }^3}xdx} $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer