#1
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Help on evaluating an integral
S(cuberoot(x))*ln(x)dx
The S is supposed to be the integral sign. It seems like it should be easy, but I can't get to the correct answer -- which according to www.calc101.com is -- (3/16)*x^(4/3)(4ln(x)-3)+C I'm assuming I need to use integration by parts, but I keep getting to the same wrong answer. I'm dumb, please help. Also, I know the answer so obviously I need to figure out the steps to get to the answer. Thank you. |
#2
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Re: Help on evaluating an integral
[ QUOTE ]
S(cuberoot(x))*ln(x)dx The S is supposed to be the integral sign. It seems like it should be easy, but I can't get to the correct answer -- which according to www.calc101.com is -- (3/16)*x^(4/3)(4ln(x)-3)+C I'm assuming I need to use integration by parts, but I keep getting to the same wrong answer. I'm dumb, please help. Also, I know the answer so obviously I need to figure out the steps to get to the answer. Thank you. [/ QUOTE ] u = ln(x) dv = x^(1/3)dx du = (1/x)dx v = (3/4)x^(4/3) S(cuberoot(x))*ln(x)dx = Su*dv = uv - Svdu + C = ln(x)*(3/4)x^(4/3) - S(3/4)x^(4/3)*(1/x)dx + C = ln(x)*(3/4)x^(4/3) - (3/4)*Sx(1/3)dx + C = ln(x)*(3/4)x^(4/3) - (3/4)*(3/4)x^(4/3) + C = ln(x)*(3/4)x^(4/3) - (3/4)^2*x(4/3) + C = (3/4)x^(4/3)*[ln(x) - 3/4] + C divide first term by 4, and multiply second term by 4: = (3/16)x^(4/3)*[4ln(x) - 3] + C. |
#3
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Fixing typos
[ QUOTE ]
S(cuberoot(x))*ln(x)dx The S is supposed to be the integral sign. It seems like it should be easy, but I can't get to the correct answer -- which according to www.calc101.com is -- (3/16)*x^(4/3)(4ln(x)-3)+C I'm assuming I need to use integration by parts, but I keep getting to the same wrong answer. I'm dumb, please help. Also, I know the answer so obviously I need to figure out the steps to get to the answer. Thank you. [/ QUOTE ] u = ln(x) dv = x^(1/3)dx du = (1/x)dx v = (3/4)x^(4/3) S(cuberoot(x))*ln(x)dx = Sudv = uv - Svdu = ln(x)*(3/4)x^(4/3) - S(3/4)x^(4/3)*(1/x)dx = ln(x)*(3/4)x^(4/3) - (3/4)*Sx^(1/3)dx = ln(x)*(3/4)x^(4/3) - (3/4)*(3/4)x^(4/3) + C = (3/4)x^(4/3)*[ln(x) - 3/4] + C To get calc101 answer, divide first term by 4, and multiply second term by 4: = (3/16)x^(4/3)*[4ln(x) - 3] + C. |
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