`int -1/sqrt(1-(4t+1)^2) dt` Find the indefinite integral

`int-1/sqrt(1-(4t+1)^2)dt`

Take the constant out,

`=-1int1/sqrt(1-(4t+1)^2)dt`

Now apply integral substitution: `u=(4t+1)`

`=>du=4dt`

`=>dt=(du)/4`

`=-1int1/sqrt(1-u^2)(du)/4`

`=-1/4int1/sqrt(1-u^2)du`

Now use the common integral: `int1/sqrt(1-x^2)dx=arcsin(x)`

`=-1/4arcsin(u)`

Substitute back `u=(4t+1)` and add a constant C to the solution,

`=-1/4arcsin(4t+1)+C`

Comments

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