Substitution
Substitution:
The u substitution:
ex.
ò 2x(x2 + 3)2 dx
Substitute u = x2 + 3 and take its derivative with respect to x, du = 2x dx.
So the integral becomes;
ò u2 du = u3/3 + C
Once the solution has been found in terms of u, substitute back into terms of x, therefore the final solution is:
ò 2x(x2 + 3)2 dx = (x2 + 3)3/3 + C
ex.
ò x(x2 + 3)2 dx
Substitute:
u = x2 + 3
du = 2x dx
x dx = 1/2 du
The integral becomes:
The final solution is:
x(x2 + 3)2 dx = 
ex.
Substitute:
| u2 = x - 1 | u2+ 1 = x |
2u du = dx
The integral becomes:
ò (u2 + 11) u · 2u du
ò (u2 + 1) 2u2 du
ò 2u4 + 2u2 du
The final solution is:
Subject:
Calculus [1]
Subject X2:
Calculus [1]