diff --git a/chapters/ch07_laplace_transforms.tex b/chapters/ch07_laplace_transforms.tex
index 1f02ef4..30f7b1a 100644
--- a/chapters/ch07_laplace_transforms.tex
+++ b/chapters/ch07_laplace_transforms.tex
@@ -130,7 +130,7 @@ The following table collects the most commonly used Laplace transforms. Each ent
     $e^{at}\sin(bt)$ & $\dfrac{b}{(s-a)^2 + b^2}$ & $s > a$ \\[10pt]
     $e^{at}\cos(bt)$ & $\dfrac{s-a}{(s-a)^2 + b^2}$ & $s > a$ \\[10pt]
     $\sin^2(bt)$ & $\dfrac{2b^2}{s(s^2 + 4b^2)}$ & $s > 0$ \\[10pt]
-    $\cos^2(bt)$ & $\dfrac{s^2}{(s^2 + 4b^2)(s)}$ & $s > 0$ \\[10pt]
+    $\cos^2(bt)$ & $\dfrac{s^2+2b^2}{s(s^2 + 4b^2)}$ & $s > 0$ \\[10pt]
     $t\sin(bt)$ & $\dfrac{2bs}{(s^2 + b^2)^2}$ & $s > 0$ \\[10pt]
     $t\cos(bt)$ & $\dfrac{s^2 - b^2}{(s^2 + b^2)^2}$ & $s > 0$ \\[10pt]
     $u_c(t)$ \quad (Heaviside step) & $\dfrac{e^{-cs}}{s}$ & $s > 0$ \\[10pt]
@@ -843,15 +843,15 @@ The inner integral is $G(s)$, and the remaining integral is $F(s)$. Thus the res
   \[
     \begin{aligned}
       \int_0^t \tau\,\sin(t-\tau)\,\diff\tau
-      &= \Bigl[-\tau\cos(t-\tau)\Bigr]_0^t + \int_0^t \cos(t-\tau)\,\diff\tau \\
-      &= \bigl(-t\cos(0) - 0\bigr) + \Bigl[-\sin(t-\tau)\Bigr]_0^t \\
-      &= -t + \bigl(-\sin(0) + \sin(t)\bigr) \\
-      &= \sin(t) - t.
+      &= \Bigl[\tau\cos(t-\tau)\Bigr]_0^t - \int_0^t \cos(t-\tau)\,\diff\tau \\
+      &= \bigl(t\cos(0) - 0\bigr) - \Bigl[-\sin(t-\tau)\Bigr]_0^t \\
+      &= t - \bigl(-\sin(0) + \sin(t)\bigr) \\
+      &= t - \sin(t).
     \end{aligned}
   \]
   Therefore:
   \[
-    \mathcal{L}^{-1}\left\{\frac{1}{s^2(s^2+1)}\right\} = \sin(t) - t.
+    \mathcal{L}^{-1}\left\{\frac{1}{s^2(s^2+1)}\right\} = t - \sin(t).
   \]
 \end{workedexample}