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`int(xcostheta+1)/((x^(2)+2xcostheta+1)^((3)/(2)))dx` isA. `sqrt(xcostheta+1)+C`B. `(1)/(sqrt(x^(2)2xcostheta+1))+C`C. `(x)/(x^(2)+2xcostheta+1))+C`D. `sqrt(x^(2)+2xcostheta+1)+C` |
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Answer» Correct Answer - C `int(xcostheta+1)/((x^(2)+2xcostheta+1)^((3)/(2)))dx=` `int((1)/(x^(2))costheta+(1)/(x^(3)))/((1+(2)/(x)costheta+(1)/(x^(2)))^((3)/(2)))dx` let `1+(2)/(x)costheta+(1)/(x^(2))=t^(2)` `(-(2)/(x^(2))costheta-(2)/(x^(3)))dx=2tdt` `1=-int(t)/(t_(3))dt=(1)/(t)+C=(1)/(sqrt(1+(2)/(x)costheta+(1)/(x^(2)))+C` |
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