Grade 12Integral Calculus

integrate the following integral
∫ (x + 1) / sqrt(2x + 3) dx

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

Ans:
Hello Student,
Please find answer to your question below

$I = \int \frac{x+1}{\sqrt{2x+3}}dx$
$I = \frac{1}{2}\int \frac{2x+2}{\sqrt{2x+3}}dx$
$I = \frac{1}{2}\int \frac{2x+3-1}{\sqrt{2x+3}}dx$
$I = \frac{1}{2}\int [\sqrt{2x+3}-\frac{1}{\sqrt{2x+3}}]dx$
$I = \frac{1}{2}\int \sqrt{2x+3}dx-\frac{1}{2}\int \frac{1}{\sqrt{2x+3}}dx$
$I = \frac{(2x+3)^{3/2}}{3}-\frac{1}{2}\int \frac{1}{\sqrt{2x+3}}dx$
$I = \frac{(2x+3)^{3/2}}{3}-\frac{1}{2}\sqrt{2x+3}+c$