Integral dx/x^1/2+x^1/3

Asked by rraj.15266 | 6th Dec, 2017, 04:37: PM

Expert Answer:

begin mathsize 16px style integral fraction numerator dx over denominator straight x to the power of begin display style 1 half end style end exponent plus straight x to the power of begin display style 1 third end style end exponent end fraction
Put space straight x equals straight t to the power of 6
dx equals 6 straight t to the power of 5 dt
integral fraction numerator 6 straight t to the power of 5 dt over denominator begin display style open parentheses straight t to the power of 6 close parentheses to the power of 1 half end exponent end style begin display style plus end style begin display style begin display style open parentheses straight t to the power of 6 close parentheses end style to the power of 1 third end exponent end style end fraction
integral fraction numerator 6 straight t to the power of 5 dt over denominator straight t cubed plus straight t squared end fraction
6 integral fraction numerator straight t to the power of 5 over denominator straight t squared left parenthesis straight t plus 1 right parenthesis end fraction dt
6 integral fraction numerator straight t cubed over denominator straight t plus 1 end fraction dt
Integrate space it space further.
end style

Answered by Sneha shidid | 6th Dec, 2017, 05:56: PM