Integration by parts is a special emthod of integration which is used when two functions are being multiplied. They are defined as u and v accordingly, and the given formula is used to evaluate the interval.

Integration by substitution is a method to evaluate integrals by changing the variables. This method can be used when the integral is of the given form.

When the integrand is in the form of a proper fraction, the integral should be rewritten as partial fractions and then integrated using the given result.

1

Evaluate ∫1/(x + 5)dx.

2

Use integration by parts to find ∫cosx(5 + x)dx.

3

Determine the following integral: ∫3x²sin(x³ − 10x) − 10sin(x³ − 10x)dx.

4

Evaluate ∫xeˣ.

5

Integrate the area of the given rectangle.