SOLUTION: i'm not sure to select which topic. but what i learn is in topic integration. Integrate the following functions using substitution method. 1.S (x+5)^7dx 2.S 2x(x^2+3)^5dx 3.S

Algebra ->  Expressions-with-variables -> SOLUTION: i'm not sure to select which topic. but what i learn is in topic integration. Integrate the following functions using substitution method. 1.S (x+5)^7dx 2.S 2x(x^2+3)^5dx 3.S      Log On


   

Question 819287: i'm not sure to select which topic. but what i learn is in topic integration.
Integrate the following functions using substitution method.
1.S (x+5)^7dx
2.S 2x(x^2+3)^5dx
3.S ((2t+1)e^(t^2+t) dt
Integrate the following functions:
4.S (e^x+e^2x/e^x) dx
5.S (3/1+2x) dx
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Note:  int%28+x%5En%2Cdx%29=+x%5E%28n%2B1%29%2F%28n%2B1%29+%2B+C(n ≠  1)  & int%28+e%5Eu%2Cdu%29=+e%5Eu+%2BC & int%28+1%2Fu%2Cdu%29= ln|x| + C  

Integrate the following functions using substitution method.

1) int%28+green%28%28x%2B5%29%29%5E7%2Cdx%29    Let u = x+5,   %28du%29%2F%28dx%29=+1,  %28du%29=+dx Then: 

int%28+green%28%28x%2B5%29%29%5E7%2Cdx%29 = int%28+u%5E7%2Cdu%29+=+u%5E8%2F8+%2B+C+=+highlight%28%28x%2B5%29%5E8%2F8+%2BC%29 

2) int%28+2x%28green%28x%5E2%2B3%29%29%5E5%2Cdx%29  Let u = x^2+3, %28du%29=+2x%28dx%29Then:

int%28+2x%28green%28x%5E2%2B3%29%29%5E5%2Cdx%29 = int%28+u%5E5%2Cdu%29=+u%5E6%2F6+%2B+C+=+highlight%28+%28x%5E2%2B3%29%5E6%2F6++%2B+C%29 

3) int%28+%282t%2B1%29e%5Egreen%28%28t%5E2%2Bt%29%29%2C+dt+%29   Let u = t^2+t, %28du%29%2F%28dt%29=+2t%2B1,%28du%29=+%282t%2B1%29dtThen:

int%28+%282t%2B1%29e%5Egreen%28%28t%5E2%2Bt%29%29%2C+dt+%29 = int%28+e%5Eu%2Cdu%29=+e%5Eu+%2BC+=+highlight%28+e%5E%28t%5E2%2Bt%29%2B+C%29 

4) 

5) int%28+3%2F%28green%281%2B2x%29%29%2C+dx%29+   Let u = 1 + 2x, %28du%29%2F%28dx%29=+2, %28du%29=+2%28dx%29 Then:

int%28+3%2F%28green%281%2B2x%29%29%2C+dx%29+ = %282%2F3%29%28int%28+1%2Fu%2Cdu%29%29= 2⁄3  ln|u| + C = 2⁄3 ln|1+2x| + C