Final Answer
$\frac{97}{226}$
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Step-by-step Solution
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1
Simplifying
$\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\frac{\sin\left(x\right)\sin\left(x\right)\cos\left(x\right)}{\sin\left(x\right)\sin\left(x\right)+1}dx$
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$\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\frac{\sin\left(x\right)\sin\left(x\right)\cos\left(x\right)}{\sin\left(x\right)\sin\left(x\right)+1}dx$
Learn how to solve problems step by step online. Integrate the function (sin(x)sin(x)cos(x))/(sin(x)sin(x)+1) from -pi/2 to pi/2. Simplifying. Simplify the expression inside the integral. Take the constant \frac{1}{2} out of the integral. Rewrite the trigonometric expression \frac{\sin\left(2x\right)\sin\left(x\right)}{\sin\left(x\right)^2+1} inside the integral.
Final Answer
$\frac{97}{226}$