A arapp New member Joined Dec 8, 2009 Messages 2 Dec 8, 2009 #1 Find the definite integral of the following using a suitable substitution: 1) (x^2)/sqroot(x^3-1)dx 2) xe^(x^2)dx 3) (ln(x))^(7/2)/(x)dx
Find the definite integral of the following using a suitable substitution: 1) (x^2)/sqroot(x^3-1)dx 2) xe^(x^2)dx 3) (ln(x))^(7/2)/(x)dx
G galactus Super Moderator Staff member Joined Sep 28, 2005 Messages 7,203 Dec 8, 2009 #2 Find the definite integral of the following using a suitable substitution: Click to expand... The substitutions are rather straightfroward. Nothing tricky. 1) \(\displaystyle \int \frac{x^{2}}{\sqrt{x^{3}-1}}dx\) Click to expand... Use the sub \(\displaystyle u=x^{3}, \;\ \frac{du}{3}=x^{2}dx\) 2) \(\displaystyle \int xe^{x^{2}}dx\) Click to expand... Use the sub \(\displaystyle u=x^{2}, \;\ \frac{du}{2}=xdx\) 3) \(\displaystyle \int\frac{(ln(x))^\frac{7}{2}}{x}dx\) Click to expand... Let \(\displaystyle u=ln(x), \;\ du=\frac{1}{x}dx\)
Find the definite integral of the following using a suitable substitution: Click to expand... The substitutions are rather straightfroward. Nothing tricky. 1) \(\displaystyle \int \frac{x^{2}}{\sqrt{x^{3}-1}}dx\) Click to expand... Use the sub \(\displaystyle u=x^{3}, \;\ \frac{du}{3}=x^{2}dx\) 2) \(\displaystyle \int xe^{x^{2}}dx\) Click to expand... Use the sub \(\displaystyle u=x^{2}, \;\ \frac{du}{2}=xdx\) 3) \(\displaystyle \int\frac{(ln(x))^\frac{7}{2}}{x}dx\) Click to expand... Let \(\displaystyle u=ln(x), \;\ du=\frac{1}{x}dx\)
