The calculator will find the integral/antiderivative of
(y−1)21, with steps shown.
Related calculator:
Definite and Improper Integral Calculator
Solution
Let u=y−1.
Then du=(y−1)′dy=1dy (steps can be seen »), and we have that dy=du.
The integral becomes
∫(y−1)21dy=∫u21du
Apply the power rule ∫undu=n+1un+1 (n=−1) with n=−2:
∫u21du=∫u−2du=−2+1u−2+1=(−u−1)=(−u1)
Recall that u=y−1:
−u−1=−(y−1)−1
Therefore,
∫(y−1)21dy=−y−11
Add the constant of integration:
∫(y−1)21dy=−y−11+C
Answer
∫(y−1)21dy=−y−11+CA