Question

Integral by hand

Answer 1

\[\int\limits_{0}^{3}\frac{ dx }{5x+1 }\]

Answer 2

aplly Ln

Answer 3

because derivative of function is present in numerator

Answer 4

how do i do that?

Answer 5

\[\int_{x_1}^{x_2} \frac{1}{ax+b} = [\frac{1}{a} \ln |ax+b| ]_{x_1}^{x_2}\]

Answer 6

Oh... I missed a dx over there..

Answer 7

how did you know that? is it a rule?

Answer 8

Yes.

Answer 9

so i cant use that because if the dx?

Answer 10

Eh.. I meant
\[\int_{x_1}^{x_2} \frac{1}{ax+b} dx= [\frac{1}{a} \ln |ax+b| ]_{x_1}^{x_2}\] I missed the dx in the previous comment.

Answer 11

It's a more general case of
\[\int\limits \frac{1}{x}dx = \ln|x|+C\]

Answer 12

So is this right? \[\frac{ 4\ln(2) }{5 }\]

Answer 13

Yep, that works.

Answer 14

thanks