I have some struggle to find sound solutions for these integrals.
It would give me much easier to comprehend what I have done wrong.
Thank you in advance.
Best regards
Anhard
Example 1
Example 2
Example 3
Example 4
Can use the substitution x= a tan(theta) or x= a sin(theta)
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my answer to number 3
Don't understand what you're saying about integration by parts, if you do that u-sub you're done at least when I did it. The answer is 5/9*(sin(10)-sin(7))
#4 Use x=3sin(theta).
dx=3cos(theta) dtheta.
Substituting back:
sin(theta)=x/3
tan(theta)=x/sqrt(9-x^2)
Which is
I can do #2 if that helps, not sure about the others. I used u=3x and the D I method and got 1/9*(sin(u)-ucos(u))-2/3*cos(u)+c