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)

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

Which is

Thank you Phinehas. I think I forgot to substitute it frist. I will rewatch this example.

#4 Use x=3sin(theta).

dx=3cos(theta) dtheta.

Substituting back:

sin(theta)=x/3

tan(theta)=x/sqrt(9-x^2)

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))