MathematicsEasy210×since 2002Q3418The value of ∫−π2π2(1+sin2x1+πsinx) dx\int\limits_{ - {\pi \over 2}}^{{\pi \over 2}} {\left( {{{1 + {{\sin }^2}x} \over {1 + {\pi ^{\sin x}}}}} \right)} \,dx−2π∫2π(1+πsinx1+sin2x)dx isAπ2{\pi \over 2}2πB5π4{{5\pi } \over 4}45πC3π4{{3\pi } \over 4}43πD3π2{{3\pi } \over 2}23πCheck answerSkip