Question

Evaluating a Definite Integral In Exercises 21-32, evaluate the definite integral. int_0^{1/6} frac{3}{sqrt{1 - 9x^2}} dx int_0^{sqrt{3}/2} frac{1}{1 + 4x^2} dx int_3^6 frac{1}{25 + (x - 3)^2} dx int_0^{ln 5} frac{e^x}{1 + e^{2x}} dx int_{pi/2}^pi frac{sin x}{1 + cos^2 x} dx int_0^{1/sqrt{2}} frac{arcsin x}{sqrt{1 - x^2}} dx int_0^{sqrt{2}} frac{1}{sqrt{4 - x^2}} dx int_{sqrt{3}}^3 frac{1}{xsqrt{4x^2 - 9}} dx int_1^4 frac{1}{xsqrt{16x^2 - 5}} dx int_{ln 2}^{ln 4} frac{e^{-x}}{sqrt{1 - e^{-2x}}} dx int_0^{pi/2} frac{cos x}{1 + sin^2 x} dx int_0^{1/sqrt{2}} frac{arccos x}{sqrt{1 - x^2}} dx

          Evaluating a Definite Integral In Exercises 21-32,
evaluate the definite integral.
int_0^{1/6} frac{3}{sqrt{1 - 9x^2}} dx
int_0^{sqrt{3}/2} frac{1}{1 + 4x^2} dx
int_3^6 frac{1}{25 + (x - 3)^2} dx
int_0^{ln 5} frac{e^x}{1 + e^{2x}} dx
int_{pi/2}^pi frac{sin x}{1 + cos^2 x} dx
int_0^{1/sqrt{2}} frac{arcsin x}{sqrt{1 - x^2}} dx
int_0^{sqrt{2}} frac{1}{sqrt{4 - x^2}} dx
int_{sqrt{3}}^3 frac{1}{xsqrt{4x^2 - 9}} dx
int_1^4 frac{1}{xsqrt{16x^2 - 5}} dx
int_{ln 2}^{ln 4} frac{e^{-x}}{sqrt{1 - e^{-2x}}} dx
int_0^{pi/2} frac{cos x}{1 + sin^2 x} dx
int_0^{1/sqrt{2}} frac{arccos x}{sqrt{1 - x^2}} dx

$Evaluating a Definite Integral In Exercises 21-32, evaluate the definite integral. int0^1/6 frac3sqrt1 - 9x^2 dx int0^sqrt3/2 frac11 + 4x^2 dx int3^6 frac125 + (x - 3)^2 dx int0^ln 5 frace^x1 + e^2x dx intpi/2^pi fracsin x1 + cos^2 x dx int0^1/sqrt2 fracarcsin xsqrt1 - x^2 dx int0^sqrt2 frac1sqrt4 - x^2 dx intsqrt3^3 frac1xsqrt4x^2 - 9 dx int1^4 frac1xsqrt16x^2 - 5 dx intln 2^ln 4 frace^-xsqrt1 - e^-2x dx int0^pi/2 fraccos x1 + sin^2 x dx int0^1/sqrt2 fracarccos xsqrt1 - x^2 dx$

Added by John S.

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