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Use the substitution method to transform the integrand into a rational function of t.

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Use the substitution method to transform the integrand into a rational function of t and then evaluate the function.

asked Jan 29, 2015 in CALCULUS by anonymous

1 Answer

0 votes

Step 1 :

The integral is image.

Evaluate the integral by substitution.

Let , then

image

If , then .

Step 2 :

Substitute corresponding values in image.

Step 3 :

Solve the above integral by using partial fractions.

Partial fraction decomposition.

image

Equate t coefficients and equate constants.

image

Multiply equation (2) by 2 and then subtract two equations.

image

Substitute image in equation (2).

image

Substitute image and imagein equation (1).

image

Step 4 :

image

Apply formula : .

image

Substitute .

image

image.

Solution :

image.

answered Jan 29, 2015 by lilly Expert
edited Jan 29, 2015 by lilly

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