help@askiitians.com

+91-87964 74404

Grade 12Integral Calculus

Integration x^2 (xsec^2x+tanx)/(xtanx+1)dx equals1. -x^2/(xtanx+1)+c2. 2log|xsinx+cosx|+c3. --×^2/(xtanx+1)+2log|xsinx+cosx|+c

Naboneeta Sarkar

9 Years agoGrade 12

2 Answers

jagdish singh singh

9 Years ago

$\hspace{-0.7 cm}$Let $I = \int x^2\cdot \left(\frac{x\sec^2 x+\tan x}{x\tan x+1}\right)dx,$ Using $\bf{I.B.P}$ and\\\\\\ Put $x\tan x+1 = t\;,$ Then $(x\sec^2 x+\tan x)dx = dt$\\\\\\ $I = x^2 \int \frac{1}{t}dt-2\int \left(x\int\frac{1}{t}dt\right)dx = \frac{x^2}{x\tan x+1}-2\int\frac{x}{x\tan x+1}dx$\\\\\\ So $I = \frac{x^2}{x\tan x+1}-2\int\frac{x\cos x}{x\sin x+\cos x}dx$$

jagdish singh singh

9 Years ago

Above process is wrong , May be you mean $\displaystyle \int x^2 \cdot \frac{x\sec^2 x+\tan x}{(x\tan x+1)^2}dx$$

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