[email protected]

+91-87964 74404

Grade 11Integral Calculus

Plz solve this integration..............

∫ ((√((x)^2+x+1))/(x+1)) dx

Sir in this,

x²+x+1 = (x+1)² - x

where x+1 is replaced by t

then we get

((v((t)^2-(t-1)))/t) dt right; then how to proceed sir.....

where 'v' represents sq.rt

Moni RS

16 Years agoGrade 11

1 Answer

Jitender Singh

12 Years ago

Ans:

$I = \int \frac{\sqrt{x^{2}+x+1}}{x+1}dx$

$I = \int \frac{\sqrt{(x+\frac{1}{2})^{2}+\frac{3}{4}}}{x+1}dx$

$u = x + \frac{1}{2}$

$du = dx$

$I = \int \frac{\sqrt{(u)^{2}+\frac{3}{4}}}{u+\frac{1}{2}}du$

$u = \frac{\sqrt{3}}{2}tan(s)$

$du = \frac{\sqrt{3}}{2}sec^{2}(s).ds$

$I = \frac{3}{4}\int \frac{sec^{3}(s)}{\frac{\sqrt{3}}{2}tan(s)+\frac{1}{2}}ds$

$t = tan (\frac{s}{2})$

$dt = \frac{1}{2}sec^{2} (\frac{s}{2}).ds$

$I = 3\int \frac{(p^{2}+1)^{2}}{(p^{2}-1)^{2}.(-p^{2}+2\sqrt{3}p+1)}dp$

Use simply partial fraction rule here, you will get

$I = \sqrt{x^{2}+x+1}-log(2 \sqrt{x^{2}+x+1}-(x-1))+log(x+1)-\frac{1}{2}sinh^{-1}(\frac{2x+1}{\sqrt{3}}) + c$

Thanks & Regards

Jitender Singh

IIT Delhi

askIITians Faculty

The area of a square field is 640000cm².what is its area in hectares

integral calculus

1 Answer Available

Last Activity: 3 Years ago

Please solve this integration. I am facing difficulty in it
How to solve this. Please solve anyone. Humble request

integral calculus

1 Answer Available

Last Activity: 4 Years ago

Using laplace transform, solve d²y/dt²+ dy/dt = t² +2t given that y=4 and y’=-2 and t=0

integral calculus

1 Answer Available

Last Activity: 4 Years ago

If 4th term of an A.p is zero, show that the 8th term is double the 6th term

integral calculus

1 Answer Available

Last Activity: 4 Years ago

View all Questions