Using the definition of the natural logarithm and the change of variable formula, the following indefinite integral may be evaluated as
I=\int (f^(')(x))/(f(x))dx=ln|f(x)|+C.
Note: Remember to write your answers using Matlab syntax. For example,
ln|x^(2)+cosx+sinh^(2)x|
would be written as Using the formula above, evaluate the following integrals: (i)
\int (5)/(5x+4)dx=
(ii)
\int (10x+5)/(5x^(2)+5x+4)dx=
B
+C
. (iii)
\int tanhxdx=

OB+C
(iv)
\int tanxdx=1
Q ?
+C
.

Question

Using the definition of the natural logarithm and the change of variable formula, the following indefinite integral may be evaluated as

I=\int (f^(')(x))/(f(x))dx=ln|f(x)|+C.

Note: Remember to write your answers using Matlab syntax. For example,

ln|x^(2)+cosx+sinh^(2)x|

would be written as Using the formula above, evaluate the following integrals: (i)

\int (5)/(5x+4)dx=

(ii)

\int (10x+5)/(5x^(2)+5x+4)dx=

B

+C

. (iii)

\int tanhxdx=

OB+C

(iv)

\int tanxdx=1

Q ?

+C

.

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