IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

senujjwal

_{[ ]}

^{[ ]}dx/{x(xⁿ+1)}=?

(a) 1/2 log(1+x²)+C (b) log(xⁿ)+C (c) log(1+xⁿ)+C (d)none of the above

minikhanna

answer to first question

_{[ ]}

^{[ ]} ^{dx/{x(x^n + 1)}}

^{first from the denominator take x^n common}

^{then it will change to}

^{x^(n+1) {1+ 1/(x^n)}}

^{put 1+1/(x^n) = t}

^{and solve u will get the answer}

^{i hope u undestood.....plz reply}

LAMPARD

its d...
_{[ ]}

^{[ ]} dx/{x(xⁿ+1)}...
multiply n divide by n...
1/n * _{[ ]}

^{[ ]} n*dx/{x(xⁿ+1)}....
put x^n=t..
nx^ndx/x=dt...
ndx/x=dt/x^n...
ndx/x=dt/t...
subst ndx/x in de integral..
u get..
1/n * _{[ ]}

^{[ ]}dt/{t(t+1)}...
1/n* _{[ ]}

^{[ ]}(1/t -1/t+1)dt...
1/n*(log t - log(t+1))...
1/n*log(t/t+1)...
1/n*log{x^n/(x^n+1)} +c....
hey guyz plzzz rate me if dis is correct...

punterjack

i think the answer slould be d cos none of the options are matching with the answers