Leadership

Mathematics

Test your understanding of this lesson Some trigonometric substitutions | Part-1:-

1)
For \(\int \frac{e^{x}}{x}(x\log_{}{x}+1)dx\), substitution is
  • \(x\log_{}{x}=z\)
  • \(e^{x}logx=z\)
  • \(\frac{1}{x}=z\)
  • \(\frac{e^{x}}{x}=z\)
2)
\(\frac{f'(x)}{f(x)}dx\) is
  • f(x)f'(x)+c
  • logf(x)+c
  • log|f'(x)|+c
  • log|f(x)|+c
3)
\(\int cosec\, xdx\) is
  • \(cosecx\,cotx+c\)
  • \(log|tan\frac{x}{2}|+c\)
  • \(log|cot\frac{x}{2}|+c\)
  • \(cosecx-cot^{2}x+c\)
4)
\(\int tanxdx\) is
  • -log|cosx|+c
  • -log|sinx|+c
  • log|cosx|+c
  • log|sinx|+c
5)
Substitution of \(e^{x}\){\(\phi(x)\)+\(\phi'(x)\)}dx is
  • \(\phi(x)=z\)
  • \(e^{x}=z\)
  • \(e^{x}\phi(x)=z\)
  • \(\frac{1}{2}e^{x}\phi(x)=z\)
Hand draw

Hide

Forgot your password?

Close

Error message here!

Hide

Lost your password? Please enter your email address. You will receive a link to create a new password.

Back to log-in

Close