Solve the following integrals:

Exercise 1


Exercise 2


Exercise 3


Exercise 4


Exercise 5


Exercise 6


Exercise 7


Exercise 8


Exercise 9


Exercise 10


Exercise 11


Exercise 12


Solution of exercise 1

Solution of exercise 2

Solution of exercise 3

Solution of exercise 4

Solution of exercise 5

Equal the coefficients of the two members.

The first integral is of logarithmic type and the second has to be broken in two.

Multiply by 2 in the second integral.

The 2 in the numerator of the second integral transforms into 1 + 1.

Decompose the second integral into two others.

Solve the first two integrals.

Transform the denominator of a squared binomial.

Multiply the numerator and denominator by 4/3, to obtain one in the denominator.

Under the squared binomial, multiply by the square root of 4/3.

Solution of exercise 6

Add and subtract 3 in the numerator, decompose into two fractions and in the first one remove common factor 3.

Multiply and divide in the first fraction by 2.

Transform the denominator of a squared binomial.

Realize a change of variable.

Solution of exercise 7

Solution of exercise 8

Solution of exercise 9

Integrate by parts.

Make the second integral.

Solution of exercise 10

Solution of exercise 11

Solution of exercise 12

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