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`int(sin^(6)x+cos^(6)x+3sin^(2)x cos^(2)x)dx` is equal toA. `x+C`B. `(3)/(2)sin2x+C`C. `-(3)/(2)cos 2x+C`D. `(1)/(3)sin 3x -cos 3x+C` |
Answer» Correct Answer - A Let `l=int(sin^(6)x+cos^(6)x+3sin^(2)x cos^(2)x)dx` `=int{(sin^(2)x)^(3)+(cos^(2)x)^(3)+3sin^(2)x cos^(2)x}dx` `=int[{:((sin^(2)x+cos^(2)x)"("sin^(4)x+cos^(4)x),(-sin^(2)xcos^(2)x")"+3sin^(2)x cos^(2)x):}]` `=int[{:((sin^(2)x+cos^(2)x)^(2)-3sin^(2)x cos^(2)x),(" "+3sin^(2)xcos^(2)x):}]` `=int1dx=x+C` |
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