let2x-1-t-x-t-1-2-dx-dt-2-t-1-t-2dt-2-1-4-t-t-t-dt-continue-it-

Question Number 7819 by akmishra last updated on 17/Sep/16

l e t 2 x + 1 = t

x = (t - 1) / 2

d x = d t / 2

\int (t - 1) \sqrt{t} / 2 d t / 2

1 / 4 \int (t \sqrt{t} - \sqrt{t}) d t

c o n t i n u e \dots . . i t . .

Answered by prakash jain last updated on 02/Oct/16

1 / 4 \int (t \sqrt{t} - \sqrt{t}) d t

= \frac{1}{4} \int (t^{3 / 2} - t^{1 / 2}) d t

= \frac{1}{4} (\frac{t^{5 / 2}}{5 / 2} - \frac{t^{3 / 2}}{3 / 2}) = \frac{1}{10} t^{5 / 2} - \frac{1}{6} t^{3 / 2} + C