How do you integrate? int(2x - 2)/(sqrtx +1) dx

int(2x - 2)/(sqrtx +1) dx

2 Answers
Apr 7, 2018

I=4/3x^(3/2)-2x+C

Explanation:

We want to integrate

I=int(2x-2)/(sqrt(x)+1)dx

Rewrite the integrand

I=2int(x-1)/(sqrt(x)+1)dx

color(white)(I)=2int((sqrt(x)+1)(sqrt(x)-1))/(sqrt(x)+1)dx

color(white)(I)=2intsqrt(x)-1dx

Integrate by the power rule

I=2(2/3x^(3/2)-x)+C

color(white)(I)=4/3x^(3/2)-2x+C

Apr 7, 2018

I=4/3x^(3/2)-2x+c

Explanation:

Here,

I=int(2x-2)/(sqrtx+1)dx

=2int(x-1)/(sqrtx+1)dx

=2int[((sqrtx)^2-(1)^2)/(sqrtx+1)]dx

=2int((sqrtx-1)cancel((sqrtx+1)))/cancel((sqrtx+1))dx

=2int(sqrtx-1)dx

=2int(x^(1/2)-1)dx

=2[x^(3/2)/(3/2)-x]+c

=4/3x^(3/2)-2x+c