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I Need Help With Integrals

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manuel1978's picture
Joined: Nov 2006
I Need Help With Integrals

I have homework and i don't have a clue of how to solve this problems. it says evaluate the following integrasl

(x^2(4x^3 + 7)^1) dx

((x^3+ 8) / (x + 2)) dx

(x + sin(5x)) dx

bananasortacos's picture
Joined: Nov 2006

are you in ab or bc?

dfdslx0988's picture
Joined: Sep 2005

(x^2(4x^3 + 7)^1) dx

Y'= U'V+UV'
Y'= 2x(4x^3+7) + x^2(12x^2)
product rule on outside function x^2 = 2x
chain rule on inside function (4x^3 + 7)^1 = 12x^2
Y'= 2x[(4x+7) + 6x(x^2)]
factor 2x and simplify
Y'= 2x(10x^3+7)

i wish i could be sure of my calculus so u might wanna check this one

((x^3+ 8) / (x + 2)) dx

Y'= U'V - UV' / V^2
Y'= 3x^2(x+2) - (x^3 + 8) 1 / (x + 2)^2
(-x^3 + 3x^2 + 8) / x + 2

(x + sin(5x)) dx

Y'= product rule + trig integrals & chain rule
Y'= 1 + cos(5x) (5)
derivative of sin = cos
chain rule on 5x
Y'= 1 + 5cos(5x)

oh, & r u in AB or BC?? what's ur book???

i misunderstood the question
what u actually want is the

"integral ot the power function"

"to integrate a power, increase the exponent by i, then divide by the mew exponent, and add c"

S u^n du = (1 / (n + 1)) u^(n + 1) + C
S = integral sign
easy, just follow the rule above and u'll get it no need for my help here pal
if u'r not sure of ur answer then take the derivative of it and u should get the exact same formula u started with

so basically ur just looking for the antiderivative

:D Cal Golden Bears, HERE I COME!!!:D

:D Go Bears!!!!:D

pianogirl2422's picture
Joined: Mar 2005

Please use the edit button next time dfdslx0988....

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