Grade 12Integral Calculus

integrate the following integral
∫ (x^2 + x + 5)/3x + 2 dx

taniska

11 Years agoGrade 12

1 Answer

Jitender Singh

11 Years ago

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

$I = \int \frac{x^2+x+5}{3x+2}dx$
$I = \frac{1}{3}\int \frac{3x^2+3x+15}{3x+2}dx$
$I = \frac{1}{3}\int \frac{3x^2+2x+x+15}{3x+2}dx$
$I = \frac{1}{3}\int \frac{x(3x+2)+x+15}{3x+2}dx$
$I = \frac{1}{3}\int xdx+\frac{1}{3}\int \frac{x+15}{3x+2}dx$
$I = \frac{x^2}{6}+\frac{1}{9}\int \frac{3x+45}{3x+2}dx$
$I = \frac{x^2}{6}+\frac{1}{9}\int \frac{3x+2+43}{3x+2}dx$
$I = \frac{x^2}{6}+\frac{1}{9}\int [1+\frac{43}{3x+2}]dx$
$I = \frac{x^2}{6}+\frac{1}{9} [x+\frac{43}{3}log(3x+2)]+c$