Integral Worksheets

Solutions

Solve the following integrals:

1 Integration Methods

2 Integration Methods

3 Integration Methods

4 Integration Methods

5 Integration Problem

6 Integration Problem

7 Integration Problem

8 Integration Problem

9 Integration Problem

10 Integration Problem

11 Integration Problem

12 Integration Problem


1

integral

derivar

Integrate

Integral Operations

Integration Solution


2

Integration Problem

Derive

Integrate

Integral Operations

Derive

Integrate

Integral Operations

Integration Solution


3

Integration Problem

Derive

Integrate

Integral Operations

Integration Solution


4

Integration Problem

Derive

Integrate

Integral Operations

Integral Operations

Integration Solution


5

Integration Problem

Integral Operations

Integral Operations

Integral Operations

Equal the coefficients of the two members.

Integral Operations

Integral Operations

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

Multiply by 2 in the second integral.

Integral Operations

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

Integral Operations

Decompose the second integral into two others.

Integral Operations

Integral Operations

Solve the first two integrals.

Integral Operations

Transform the denominator of a squared binomial.

Integral Operations

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.

Integral Operations

Integral Operations

Integral Operations

Integral Operations

Integration Solution


6

Integration Problem

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

Integral Operations

Multiply and divide in the first fraction by 2.

Integral Operations

Integral Operations

Integral Operations

Transform the denominator of a squared binomial.

Integral Operations

Integral Operations

Realize a change of variable.

Change of Variable

Integral Operations

Integration Solution


7

Integration Problem

Change of Variable

Change of Variable

Integral Operations

Integration Solution


8

Integration Problem

Change of Variable

Change of Variable

Integral Operations

Change of Variable

Integration Solution


9

Integration Problem

Change of Variable

Integral Operations

Integral Operations

Integrate by parts.

Integrate by Parts

Derive

Integrate

Integral Operations

Make the second integral.

Integral Operations

Integral Operations

Integral Operations

Integral Operations

Change of Variable

Integral Operations

Integration Solution


10

Integration Problem

Change of Variable

Integral Operations

Integration Solution


11

Integration Problem

Change of Variable

Change of Variable

Integral Operations

Integral Operations

Integration Solution


12

Integration Problem

Change of Variable

Change of Variable

Integration Solution