Can You Help Me Integrate $\sin(u) + u^6$ Correctly?

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SUMMARY

The discussion focuses on integrating the expression $\sin(u) + u^6$. A key point is the correct placement of parentheses, which simplifies the integration process. The user initially confused the expression as $\sin(u + u^6)$, leading to complications. By clarifying the correct form, the integration becomes straightforward, allowing for successful resolution of the problem.

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  • Familiarity with trigonometric functions, specifically sine.
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  • Ability to manipulate algebraic expressions and parentheses correctly.
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Untitled 3.png


Can you please help me ?
I have tried to do it many times but still got the wrong answer.
Thank you in advance.
 
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Make the substitution $t = \sin x$.
 
Opalg said:
Make the substitution $t = \sin x$.
Untitled 5.png
I am stuck here
Can you please help me ?
 
Get the parentheses in the right place! It's not $\sin(u+u^6)$, but $\sin(u) + u^6$, which is much easier to integrate.
 
Opalg said:
Get the parentheses in the right place! It's not $\sin(u+u^6)$, but $\sin(u) + u^6$, which is much easier to integrate.
Thank you very much
I understand now
 

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