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EEMajor12
 3 years ago
Integral Question
EEMajor12
 3 years ago
Integral Question

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EEMajor12
 3 years ago
Best ResponseYou've already chosen the best response.0f(x)=\int_1^{3x^5} \ln(t^2+1) \, dt

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1\[f(x)=\int_1^{3x^5} \ln(t^2+1) \, dt\]like that?

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1is the question find the derivative?

imranmeah91
 3 years ago
Best ResponseYou've already chosen the best response.0too hard to integrate

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1use the chain rule. the derivative of the integral is the integrand, so replace t by \[3x^5\] and then multiply the answer by \[15x^4\]

EEMajor12
 3 years ago
Best ResponseYou've already chosen the best response.0yeah im having trouble with these. Ill try it sat!

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1\[f'(x)=\ln((3x^5)^2+1)\times 15x^4\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1i should have let you do it on your own, but once you see it you should realize how easy it is. it is clear what i did yes?

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1if you need a word of explanation let me know

EEMajor12
 3 years ago
Best ResponseYou've already chosen the best response.0i understand chain rule for ln (function within function). where did the 15x4 come from?

EEMajor12
 3 years ago
Best ResponseYou've already chosen the best response.015x^4 \ln(9x^{10}+1) ?

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.1it is the chain rule and you have a composite function. don't forget that \[F(x)=\int_a^x f(t)dt\] is a function of "x" so if you do not have an x in the upper limit, but rather something else, you have a composition like \[F(g(x))=\int_a^{g(x)}f(t)dt\] and so you need the chain rule
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