diff --git a/docs/src/inverting_integrals.md b/docs/src/inverting_integrals.md
index 8cbfcc3e..4f0380d4 100644
--- a/docs/src/inverting_integrals.md
+++ b/docs/src/inverting_integrals.md
@@ -1,19 +1,19 @@
 # Inverting integrals
 
-Solving implicit integral problems of the form:
+Solving implicit integral problems of the following form is supported:
 
 ```math
 \begin{equation}
-    \text{find $t$ such that } \int_{t_1}^t f(\tau)\text{d}\tau = V \ge 0
+    \text{find $t$ such that } \int_{t_1}^t f(\tau)\text{d}\tau = V \ge 0,
 \end{equation}
 ```
 
-is supported for interpolations $f$ that are strictly positive and of one of these types:
+where $t_1$ is given by `first(A.t)`. This is supported for interpolations $f$ that are strictly positive and of one of these types:
 
   - `ConstantInterpolation`
   - `LinearInterpolation`
 
-This is done by creating an 'integral inverse' interpolation object which can efficiently compute $t$ for a given value of $V$, see the example below.
+This is achieved by creating an 'integral inverse' interpolation object which can efficiently compute $t$ for a given value of $V$, see the example below.
 
 ```@example inverting_integrals
 using Random #hide
diff --git a/src/integral_inverses.jl b/src/integral_inverses.jl
index 1e2ca581..4437726e 100644
--- a/src/integral_inverses.jl
+++ b/src/integral_inverses.jl
@@ -6,8 +6,8 @@ abstract type AbstractIntegralInverseInterpolation{T} <: AbstractInterpolation{T
 Creates the inverted integral interpolation object from the given interpolation. Conditions:
 
   - The range of `A` must be strictly positive
-  - There must be an ordering defined on the data type of `A.u`
-  - This is currently only supported for ConstantInterpolation and LinearInterpolation
+  - `A.u` must be a number type (on which an ordering is defined)
+  - This is currently only supported for `ConstantInterpolation` and `LinearInterpolation`
 
 ## Arguments
 
@@ -22,7 +22,16 @@ function _derivative(A::AbstractIntegralInverseInterpolation, t::Number, iguess)
 end
 
 """
-    some stuff
+    LinearInterpolationIntInv(u, t, A)
+
+It is the interpolation of the inverse of the integral of a `LinearInterpolation`.
+Can be easily constructed with `invert_integral(A::LinearInterpolation{<:AbstractVector{<:Number}})`
+
+## Arguments
+
+  - `u` : Given by `A.t`
+  - `t` : Given by `A.I` (the cumulative integral of `A`)
+  - `A` : The `LinearInterpolation` object
 """
 struct LinearInterpolationIntInv{uType, tType, itpType, T} <:
        AbstractIntegralInverseInterpolation{T}
@@ -31,9 +40,10 @@ struct LinearInterpolationIntInv{uType, tType, itpType, T} <:
     extrapolate::Bool
     idx_prev::Base.RefValue{Int}
     itp::itpType
+    safetycopy::Bool
     function LinearInterpolationIntInv(u, t, A)
         new{typeof(u), typeof(t), typeof(A), eltype(u)}(
-            u, t, A.extrapolate, Ref(1), A)
+            u, t, A.extrapolate, Ref(1), A, A.safetycopy)
     end
 end
 
@@ -56,7 +66,16 @@ function _interpolate(
 end
 
 """
-    some stuff
+    ConstantInterpolationIntInv(u, t, A)
+
+It is the interpolation of the inverse of the integral of a `ConstantInterpolation`.
+Can be easily constructed with `invert_integral(A::ConstantInterpolation{<:AbstractVector{<:Number}})`
+
+## Arguments
+
+  - `u` : Given by `A.t`
+  - `t` : Given by `A.I` (the cumulative integral of `A`)
+  - `A` : The `ConstantInterpolation` object
 """
 struct ConstantInterpolationIntInv{uType, tType, itpType, T} <:
        AbstractIntegralInverseInterpolation{T}
@@ -65,9 +84,10 @@ struct ConstantInterpolationIntInv{uType, tType, itpType, T} <:
     extrapolate::Bool
     idx_prev::Base.RefValue{Int}
     itp::itpType
+    safetycopy::Bool
     function ConstantInterpolationIntInv(u, t, A)
         new{typeof(u), typeof(t), typeof(A), eltype(u)}(
-            u, t, A.extrapolate, Ref(1), A
+            u, t, A.extrapolate, Ref(1), A, A.safetycopy
         )
     end
 end