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help? [integrals]?

0 votes

asked May 15, 2015 in CALCULUS by anonymous

4 Answers

0 votes

(5)

Step 1:

The integral is .

Sum and difference rule of integral : .

Integral formula of sine function : .

Integral formula of exponential function : .

                            

.

Solution :

.

answered May 15, 2015 by joseph Apprentice
0 votes

(6)

Step 1:

The integral is .

Rewrite the integral.

Consider .

Substitute and in the above integral.

                        

Power rule of integral formula : image.

                       

Replace in the above expression.

                       

.

Solution :

.

answered May 15, 2015 by joseph Apprentice
0 votes

(7)

Step 1:

The integral is .

Consider .

Substitute and  in the above integral.

Power rule of integral formula : image.

                       image

Replace in the above expression.

                      

image.

Solution :

image.

answered May 15, 2015 by joseph Apprentice
edited May 15, 2015 by joseph
0 votes

(8)

Step 1:

The integral is .

Rewrite the integral.

Consider the function image.

Now use the partial fraction method :

Compare the coefficients of x terms.

                    (1)

Compare the constant terms.

            (2)

Multiple equation (1) with 3.

             (3)

Slove equation (2) and (3).

.

Substitute in equation (1).

image.

Step 2:

image

Integral of logarithm function : .

                              image

image.

Solution :

image.

answered May 15, 2015 by joseph Apprentice
edited May 15, 2015 by joseph

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