How do I solve this integrals?(dy/secˆ2(y))(dx/(-xˆ2 + x))

[FrostScYthe]

How do I solve this integrals?

(dy/secˆ2(y))

(dx/(-xˆ2 + x))

 

[marlon]

How do I solve this integrals?

(dy/secˆ2(y))

Partial integration or use the formula's linking cos(x) to cos(2x)

(dx/(-xˆ2 + x))

Partial fractions .

marlon

 

[VietDao29]

How do I solve this integrals?

(dy/secˆ2(y))

(dx/(-xˆ2 + x))

#1, $$\int \frac{dy}{\sec ^ 2 y} = \int \frac{dy}{\frac{1}{\cos ^ 2 y}} = \int \cos ^ 2 y dy$$
Now, do you know the Double-angle formulae?
#2, I'll give you a hint, try to complete the square in the denominator, then use u-substitution, and it's done:
$$\int \frac{dx}{-x ^ 2 + x} = - \int \frac{dx}{x ^ 2 - x}$$
Can you go from here? :)