Generating...                               ibee2025_n9

  1. Find $\displaystyle \int {{{1}\over{\sqrt{3\,x+5}}}}{\;dx}$ by using substitution.

    $\displaystyle 2\,\sqrt{3\,x+5} + C$ $\displaystyle {{2\,\sqrt{3\,x+5}}\over{3}} + C$ $\displaystyle -{{2\,\sqrt{3\,x+5}}\over{3}} + C$ $\displaystyle -2\,\sqrt{3\,x+5} + C$ $\displaystyle -{{2}\over{\sqrt{3\,x+5}}} + C$

  2. Find $\displaystyle \int {\sec x}{\;dx}$.

    $\displaystyle \sin x-x\,\cos x + C$ $\displaystyle -\ln \left(\csc x+\cot x\right) + C$ $\displaystyle \ln \left(\tan x+\sec x\right) + C$ $\displaystyle {{\sin \left(2\,x\right)-2\,x\,\cos \left(2\,x\right)}\over{8}} + C$ $\displaystyle x\,\sin x+\cos x + C$ $\displaystyle -{{\cos ^2x}\over{2}} + C$

  3. Find $\displaystyle \int {{{x^2+1}\over{\sqrt{x}}}}{\;dx}$.

    $\displaystyle {{2\,x^{{{5}\over{2}}}+10\,\sqrt{x}}\over{5}} + C$ $\displaystyle 2\,\sqrt{x} + C$ $\displaystyle {{\left(x^2+1\right)^2}\over{x}} + C$ $\displaystyle {{x^3}\over{3}}+x + C$

  4. Find $\displaystyle \int {{{1}\over{\sqrt{9-x^2}}}}{\;dx}$.

    $\displaystyle {\rm asinh}\; \left({{x}\over{3}}\right) + C$ $\displaystyle \arcsin \left({{x}\over{3}}\right) + C$ $\displaystyle {{\ln \left(x^2+9\right)}\over{2}} + C$ $\displaystyle {{\arctan \left({{x}\over{3}}\right)}\over{3}} + C$ $\displaystyle {{\ln \left(x+3\right)}\over{6}}-{{\ln \left(x-3\right)}\over{6}} + C$ $\displaystyle \ln \left(2\,\sqrt{x^2-9}+2\,x\right) + C$

  5. Find $\displaystyle \int {x\,\ln x}{\;dx}$ by using integration by parts.

    $\displaystyle {{x^3\,\ln x}\over{3}}-{{x^3}\over{9}} + C$ $\displaystyle x\,\ln x-x + C$ $\displaystyle -{{\ln x}\over{x}}-{{1}\over{x}} + C$ $\displaystyle {{x^2\,\ln x}\over{2}}-{{x^2}\over{4}} + C$ $\displaystyle {{2\,x^{{{3}\over{2}}}\,\ln x}\over{3}}-{{4\,x^{{{3}\over{2}}} }\over{9}} + C$ $\displaystyle 2\,\sqrt{x}\,\ln x-4\,\sqrt{x} + C$


Department of Mathematics
Last modified: 2026-05-20