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
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Solution of exercise 2
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Solution of exercise 3
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Solution of exercise 4
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Solution of exercise 5
Equal the coefficients of the two members.
0 = A + M 1 = A + M + N 0 = A + N A = -1, M = 1, N = 1
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
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Solution of exercise 9
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Make the second integral.
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Solution of exercise 10
Solution of exercise 11
Solution of exercise 12
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