Mn ơi giúp e câu c,d,e với ạ

Đáp án:

$\begin{array}{l}
c)\int\limits_0^{\pi /4} {{{\cos }^2}x.{{\sin }^3}xdx} \\
 = \int\limits_0^{\pi /4} {{{\cos }^2}x.{{\sin }^2}x.\sin xdx} \\
 = \int\limits_0^{\pi /4} {{{\cos }^2}x.\left( {1 - {{\cos }^2}x} \right)\left( { - d\cos x} \right)} \\
 = \int\limits_0^{\pi /4} {{{\cos }^4}x - {{\cos }^2}xd\cos x} \\
 = \left( {\frac{1}{5}{{\cos }^5}x - \frac{1}{3}{{\cos }^3}x} \right)_0^{\pi /4}\\
 = 0,05\\
d)\int\limits_0^{\pi /4} {\frac{{{{\sin }^3}x}}{{{{\cos }^2}x}}dx} \\
 = \int\limits_0^{\pi /4} {\frac{{{{\cos }^2}x - 1}}{{{{\cos }^2}x}}d\cos x} \\
 = \int\limits_0^{\pi /4} {1 - \frac{1}{{{{\cos }^2}x}}d\cos x} \\
 = \left( {{\mathop{\rm cosx}\nolimits}  + \frac{1}{{\cos x}}} \right)_0^{\pi /4} = \frac{{3\sqrt 2  - 4}}{2}
\end{array}$