Posted by
**Chelsea** on
.

Find the antiderivative by hand in each case.

S stands for the integral sign

A) S x*sqrt(10 + x^2) dx

So, u= 10 + x^2

du= 2xdx

du/2= xdx

(1/2) S sqrt(u) du

(1/2)*((u^(3/2))/(3/2))

(1/2)*(2/3)*(u^(3/2))

(1/3)*(u^(3/2))

= (1/3)*(10 + x^2)^(3/2) correct/incorrect?

B) S (x/(sqrt(2 - 3x)))dx

S (x)*(2 - 3x)^(-1/2)

u= 2 - 3x

du= -3dx

du/-3=dx

x= -((u - 2)/3)

=(-1/3) S (-((u - 2)/3))*(u^(-1/2))

=(-1/3) S ((-((u^(1/2)/3)-((2u^(-1/2))/3))

=(-1/3)*[((2/9)*(u^(3/2))-((4/3)*(u^(1/2))]

=[(-2/27)*((2 - 3x)^(3/2)) + (4/3)*((2 - 3x)^(1/2))] correct/incorrect?