Integration of x/(2x+5)?
2 Answers
Apr 7, 2018
I=1/4((2x+5)-5ln(abs((2x+5))))+C
Explanation:
We want to solve
I=intx/(2x+5)dx
Make a substitution
I=1/2intx/udu
But
I=1/2int((u-5)/2)/udu
color(white)(I)=1/4int(u-5)/udu
color(white)(I)=1/4int1-5/udu
color(white)(I)=1/4(u-5ln(abs(u)))+C
Substitute back
I=1/4((2x+5)-5ln(abs((2x+5))))+C
Apr 7, 2018
Let
Therefore,
Also,