The integral of (x^6)(e^x7) I did x^7/7 U=e^x7 Where do I go from here?
K KEYWEST17 New member Joined Jan 19, 2011 Messages 46 Jan 19, 2011 #1 The integral of (x^6)(e^x7) I did x^7/7 U=e^x7 Where do I go from here?
S soroban Elite Member Joined Jan 28, 2005 Messages 5,586 Jan 19, 2011 #2 Hello, KEYWEST17! \(\displaystyle \text{Recall that: }\;\int e^u\,du \:=\:e^u + C\) \(\displaystyle \displaystyle \int x^6e^{x^7}\,dx\) Click to expand... \(\displaystyle \text{We have: }\,\int e^{x^7}\left(x^6\,dx)\) \(\displaystyle \text{Let: }\:u \,=\,x^7 \quad\Rightarrow\quad du \,=\,7x^6\,dx \quad\Rightarrow\quad x^6\,dx \:=\:\tfrac{1}{7}\,du\) \(\displaystyle \text{Substitute: }\;\int e^u\left(\tfrac{1}{7}\,du\right) \;=\;\tfrac{1}{7}\int e^u\,du \;=\;\tfrac{1}{7}e^u + C\) \(\displaystyle \text{Back-substitute: }\:\tfrac{1}{7}e^{x^7} + C\)
Hello, KEYWEST17! \(\displaystyle \text{Recall that: }\;\int e^u\,du \:=\:e^u + C\) \(\displaystyle \displaystyle \int x^6e^{x^7}\,dx\) Click to expand... \(\displaystyle \text{We have: }\,\int e^{x^7}\left(x^6\,dx)\) \(\displaystyle \text{Let: }\:u \,=\,x^7 \quad\Rightarrow\quad du \,=\,7x^6\,dx \quad\Rightarrow\quad x^6\,dx \:=\:\tfrac{1}{7}\,du\) \(\displaystyle \text{Substitute: }\;\int e^u\left(\tfrac{1}{7}\,du\right) \;=\;\tfrac{1}{7}\int e^u\,du \;=\;\tfrac{1}{7}e^u + C\) \(\displaystyle \text{Back-substitute: }\:\tfrac{1}{7}e^{x^7} + C\)
