U substitution is a way to evaluate integrals that cannot be evaluated using just one of the basic integral rules. It is similar to the chain rule for derivatives.
Let's evaluate S(sqrt(7x+9))dx.
Let u=7x+9
This is an important step. You must take the derivative of u.
du=7dx.
Now, solve for dx. dx=du/7.
Now we have the integral as S(sqrt(u))*du/7.
This becomes 1/7*S(sqrt(u))du which is equivalent to
1/7*S(u)^(1/2)du. This can be integrated, resulting in
1/7*2/3*((u)^3/2)+C
simplify
2/21*(7x+9)^3/2+C.
Evaluate the following
1) S(4cos(3x))dx
2) S(e^(5x+2))dx
3) S(3x+6/(x^2+4x-3))dx.
Let's evaluate S(sqrt(7x+9))dx.
Let u=7x+9
This is an important step. You must take the derivative of u.
du=7dx.
Now, solve for dx. dx=du/7.
Now we have the integral as S(sqrt(u))*du/7.
This becomes 1/7*S(sqrt(u))du which is equivalent to
1/7*S(u)^(1/2)du. This can be integrated, resulting in
1/7*2/3*((u)^3/2)+C
simplify
2/21*(7x+9)^3/2+C.
Evaluate the following
1) S(4cos(3x))dx
2) S(e^(5x+2))dx
3) S(3x+6/(x^2+4x-3))dx.