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Indefinite Integrals

$(1).\,\,$ Evaluate $\displaystyle \int{\sin{\sqrt{x}}}\,dx$

$(2).\,\,$ Evaluate $\displaystyle \int{\dfrac{1}{\sin{x}+\cos{x}}\,} dx$

$(3).\,\,$ Evaluate $\displaystyle \int{\cos^7{x}}\,dx$

$(4).\,\,$ Evaluate $\displaystyle \int{\dfrac{1}{\sin^{\Large \frac{1}{2}}{x}\cos^{\Large \frac{3}{2}}{x}}\,} dx$

$(5).\,\,$ Evaluate $\displaystyle \int{\dfrac{sin^6{x}+\cos^6{x}}{\sin^2{x}\cos^2{x}}\,} dx$

Definite Integrals

$(1).\,\,$ Evaluate $\displaystyle \int_{0}^{\Large \frac{\pi}{2}}{\big(\sqrt{\tan{x}}+\sqrt{\cot{x}}\big)}\,dx$

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