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$\int_{\frac{\pi}{2}}^{\pi }\frac{\tan\left(x\right)}{\sin\left(x\right)^2\sec\left(x\right)+\cos\left(x\right)}dx$
Learn how to solve limits by direct substitution problems step by step online. Integrate the function tan(x)/(sin(x)^2sec(x)+cos(x)) from pi/2 to pi. Simplifying. Rewrite the trigonometric expression \frac{\tan\left(x\right)}{\sin\left(x\right)^2\sec\left(x\right)+\cos\left(x\right)} inside the integral. Apply the integral of the sine function: \int\sin(x)dx=-\cos(x). Evaluate the definite integral.