Could you please confirm my answers as correct or incorrect, if incorrect please point out errors and assist in correcting errors.(adsbygoogle = window.adsbygoogle || []).push({});

Thanks in advance

1. The problem statement, all variables and given/known data

Intergrate the following functions with respect to x using recognition, substitution or intergration by parts:

x^2(2+x^3)^4

x(x^2+2)^5

xcosx

3. The attempt at a solution

1)

integral(x^2(2+x^3)^4)

put (2+x^3) =x

thus

3x^2dx = dz

or

x^2dx = dz/3

the integral becomes

integral(z^4dz)/3

= z^5/15

=(2+x^3)^5/15 + c

2)

integral(x(x^2+2)^5)

put x^2+2=z

or

2xdx = dz

thus

xdx = dz/2

integral(z^5/2)dz

= z^6/12+c

=(x^2+2)^6/12 + c

3) integral(xcosx)

x(sinx) - integral(sinx)

= -xsinx+cosx +c

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# Homework Help: Integration problem, please help

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