InterviewSolution
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InterviewSolution
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Evaluate `intsqrt(x^(2)+3x)dx`. |
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Answer» We have `(x^(2)+3x)={x^(2)+3x+((3)/(2))^(2)-((3)/(2))^(2)}=(x+(3)/(2))^(2)-((3)/(2))^(2)`. `thereforeI=intsqrt(x^(2)+3x)dx` `=intsqrt((x+(3)/(2))^(2)-((3)/(2))^(2))dx=intsqrt(t^(2)-((3)/(2))^(2))dt "where"(x+(3)/(2))=t` `=(1)/(2)tsqrt(t^(2)-(9)/(4))-(9)/(8)log|t+sqrt(t^(2)-(9)/(4))|+C` `{"using"intsqrt(x^(2)-a^(2))dx=(x)/(2)sqrt(x^(2)-a^(2))-(a^(2))/(2)log|x+sqrt(x^(2)-a^(2))|+C}` `=(1)/(2)(x(3)/(2))sqrt(x^(2)+3x)-(9)/(8)log|(x+(3)/(2))+sqrt(x^(2)+3x)|+C`. |
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