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

$$let2x+1=t$$$$x=(t-1)/2$$$$dx=dt/2$$$$\int (t-1)\sqrt{t}/2dt/2$$$$1/4\int (t\sqrt{t}-\sqrt{t})dt$$$$continue.....it..$$$$$$$$$$$$$$

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

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

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