12.I=\int 1/[(x+1/2)^{2}+(\sqrt{3}/4)^{2}]dx
which is of the form dx/x2+a2
1.I=\int cosh^2(8x+5)dx
2.I=\int \frac{dx}{(x^2+x+1)}
3.I=\int\frac{(2+3x^2)dx}{[x^2(1+x^2)]}..
4.I=\int\frac{(x^2-1)dx}{(x^4+3x^2+1)arctan[(x^2+1)/x]}
5.I=\int \frac{(\sqrt{a^2-x^2})dx}{x^4}
plzz help me m a begginer nd post ur full solutions rather than half nd hintsplzzzzzzzzzzz[1][132][1]
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15 Answers
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1arre bhaii ye kaise kiya???????????????any method.........................or as usual it needs practice
29@Sanchit..this method is called making a pefect square..u may be familiar with it..
1these r very basics ques.........
I think u need to read the theory and formulae before proceeding......[1]
39To make perfect square, take coefficient of middle term, or x, half it and then square it and add/subtract to expression
x2 + x + 1 = x2 + x + 1/4 - 1/4 + 1 = (x + 1/2)2 -1/4 + 1 = (x + 1/2)2 + 3/4 = (x + 1/2)2 + (√3/2)2
1hey is IA maron right for beggining cozz its the first time m learning itegrals nd m studying from it
39you'll get a better hang of it from NCERT 12th class book :)
29@sanchit...Try NCERT first ..it contains around 500 problems on integration...then only proceed to any other book...
1now there fore
put 16 x + 10 = u 16 dx = du dx = du /16
now u can do it further !!!!!
other method
cosh2 x = 1 + cos h(2x ) 2
is this formula valid
1for second one
ax ^ 2 + bx + c
for completing a perfect square
first the coefficient of x 2 must be 1 .
then
ADD AND SUBTRACT ( 12 . COEFFICIENT OF X ) 2
EX .
2. x^2 + x + 1 = x ^2 + x + 1 + ( 1/2 ) ^2 - ( 1 /2 ) ^2
combine the ones in bold and others
x2+ x + 14 + 1 - 14
( x + 12 )2 + 34
1for integration after ncert
this book is best
http://www.askiitians.com/book-review/IIT-JEE-Mathematics-Arihant-Integral-Calculus
ur doubts are good they are not of basic level as u think