Evaluate \(\displaystyle\displaystyle \displaystyle\int{\,\frac{1}{\sqrt{x}{{\left( 1+\sqrt{x} \righ

Question

Evaluate $\displaystyle\displaystyle \displaystyle\int{\,\frac{1}{\sqrt{x}{{\left( 1+\sqrt{x} \right)}^{2}}}\mathrm{d}x}$. Evaluate $\displaystyle\displaystyle \displaystyle\int{\frac{4}{{{e}^{-x}}-1}\,\mathrm{d}x}$. Evaluate $\displaystyle\displaystyle \displaystyle\int{{{\left( \sin x+2\cos x \right)}^{2}}}\,\mathrm{d}x$. Evaluate $\displaystyle\displaystyle \displaystyle\int{\sec \left( 2x-5 \right)\mathrm{ d}x}$.

Accepted Answer

(c) $-\dfrac2{1+\sqrt{x}}+C$ (d) $-4\ln|1-e^x|+C$ (e) $\dfrac52x+\dfrac34\sin2x-\cos2x+C$ (f) $\dfrac12\ln|\sec(2x-5)+\tan(2x-5)|+C$

ACJC Assignment 20 Q1

ACJC Assignment 20 Q1

Video Solution:

Solution:

Solution locked