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anonymous
 5 years ago
calculate the integral of the following using:
anonymous
 5 years ago
calculate the integral of the following using:

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the standard form \[\int\limits_{}^{}f'(x)e ^{f(x)}dx=e ^{f(x)}+c , or \int\limits_{}^{}e ^{u}(du/dx)dx = e ^{u}+c\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[(a) 2xe ^{x ^{2}+3}\] \[(b)(10x2)e ^{5x ^{2}2x}\] \[(c)(3x+2)e ^{3x ^{2}+4x+1}\] \[(d)(x ^{2}2x)e ^{x ^{3}3x ^{2}}\]

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.1What have you try with these problems?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yea i have i can do (a),(b) but c and d i got the wrong answers

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.1You need to adjust a little bit for c) and d). For example in c) if you use \(u=3x^2+4x\) then \(du=6x+4=2(3x+2)\, dx\). So your integral become \(\frac{1}{2}\int e^u\, du\)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh i understand thanks but what happens to the (3x+2) inside the bracket

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.1\((3x+2)\,dx\) become \(\frac{1}{2}du\)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok so how about this one \[(6x ^{2}8x+6)e ^{x ^{3}2x ^{2}+3x5}\]

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.1what is the derivative of \(x^32x^2+3x5\) ?

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.1Good! How that derivative relates to \(6x^28x+6\) ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the coefficients are doubled

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.1Yes great! Then for \(f(x)=x^32x^2+3x5\) the integral is \(\frac{1}{2}\int f'(x)e^{f(x)}\,dx\)

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.1Sorry your were right :)

watchmath
 5 years ago
Best ResponseYou've already chosen the best response.1So \(2\int f'(x)e^{f(x)}\,dx\).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh i see how it works out now lol:) ok thanks ill have shot at the others thankyou
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