Question

integrate 1/9-16x^2​

Answer 1

Step-by-step explanation:

put x = (3/4)sin(a)

the proceed you will get your ans.

but remember to change the dx also.

if you doesn't get your ans, message me

i will give you the solution.

if question is of definite integration then change the limit also.

Answer 2

Answer

1/24{log|(3 + 4x)/(3 - 4x)|} + C

$\large \bf \underline{Given : }$

• 1/(9 - 16x²)

$\bf \large \underline{Task : }$

• To integrate 1/(9 - 16x²)

$\bf \large \underline{Formula \: to \: be \: used : }$

✪$\sf \int \dfrac{dx}{a^{2}-x^{2}} =\dfrac{1}{2a}\log| \dfrac{a+x}{a-x}| + C$

$\large \bf \underline{Solution : }$

$\sf\longrightarrow \int \dfrac{dx}{9-16x^{2}}$

$\sf\longrightarrow \int\dfrac{\dfrac{dx}{16}}{\dfrac{9-16x^{2}}{16}}$

$\sf\longrightarrow \dfrac{1}{16}\int\dfrac{dx}{(\dfrac{3}{4})^{2} - x^{2} }$

$\sf\longrightarrow \dfrac{1}{16} \{ \dfrac{1}{2\times\dfrac{3}{4}} \log|\dfrac{\dfrac{3}{4}+x}{\dfrac{3}{4} - x} |+ C \}$

$\sf\longrightarrow \dfrac{1}{24}\log|\dfrac{3+4x}{3-4x}| + C$