# Can anyone help to compute 3 integrals?

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I tried to work on them, but I can't solve with either trigonometric u substitution or partial fraction.

The problems require to using the following integral formulas:

#int(du)/sqrt(a^2-u^2)=sin^-1(u/a)#

#int(du)/sqrt(u^2+a^2)=ln(u+sqrt(u^2+a^2))# #int(du)/(u^2+a^2)=1/atan^-1(u/a)#

1.#intdx/sqrt(x^2+6x+10#

2.#int(dx)/sqrt(6x-x^2)#

3.#int(dx)/(2x^2+6x+5)#

I tried to work on them, but I can't solve with either trigonometric u substitution or partial fraction.

The problems require to using the following integral formulas:

1.

2.

3.

Answers below...

Initial integral:

The second integral

We can use the same concept here.

The third integral

Applying the same concept:

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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