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Question: Prove that $\int_{0}^{\pi / 2} \frac{\sqrt{\sin x}}{(\sqrt{\sin x}+\sqrt{\cos x})} d x=\frac{\pi}{4}$ Solution:...
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Question: Prove that $\int_{0}^{\pi / 2} \frac{\cos x}{(\sin x+\cos x)} d x=\frac{\pi}{4}$ Solution:...
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Question: Evaluate the following integrals $\int_{\pi / 6}^{\pi / 2} \frac{\operatorname{cosec} x \cot x}{1+\operatorname{cosec}^{2} x} d x$ Solution:...
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Question: Evaluate the following integrals $\int_{1}^{2} \frac{d x}{x(1+\log x)^{2}}$ Solution:...
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Question: Evaluate the following integrals $\int_{0}^{(\pi / 2)^{1 / 3}} x^{2} \sin x^{3} d x$ Solution:...
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Question: Evaluate the following integrals $\int_{\pi / 4}^{\pi / 2} \frac{\cos \theta}{\left.\cos \frac{\theta}{2}+\sin \frac{\theta}{2}\right)^{3}} d \theta$ Solution:...
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Question: Evaluate the following integrals $\int_{2}^{3} \frac{(2-x)}{\sqrt{5 x-6-x^{2}}} d x$ Solution:...
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Question: Evaluate the following integrals $\int_{0}^{\pi / 2}(\sqrt{\tan x}+\sqrt{\cot x}) d x$ Solution:...
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Question: Evaluate the following integrals $\int_{1}^{2} \frac{d x}{(x+1) \sqrt{x^{2}-1}}$ Solution:...
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Question: Evaluate the following integrals $\int_{0}^{1} \frac{\left(1-x^{2}\right)}{\left(1+x^{2}\right)^{2}} d x$ Solution:...
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Question: Evaluate the following integrals $\int_{0}^{1} x^{3} \sqrt{1+3 x^{4}} d x$ Solution:...
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Question: Evaluate the following integrals $\int_{0}^{9} \frac{\mathrm{dx}}{(1+\sqrt{\mathrm{x}})}$ Solution:...
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Question: Evaluate the following integrals $\int_{0}^{a} \sin ^{-1} \sqrt{\frac{x}{a+x}} d x$ Solution:...
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Question: Evaluate the following integrals $\int_{0}^{1} \sin ^{-1} \sqrt{x} d x$ Solution:...
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Question: Evaluate the following integrals $\int_{0}^{1} x\left(\tan ^{-1} x\right)^{2} d x$ Solution:...
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Question: Evaluate the following integrals $\int_{0}^{1}\left(\cos ^{-1} x\right)^{2} d x$ Solution:...
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Question: Evaluate the following integrals $\int_{\pi / 3}^{\pi / 2} \frac{\sqrt{1+\cos x}}{(1-\cos x)^{5 / 2}} d x$ Solution:...
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Question: Evaluate the following integrals $\int_{0}^{\pi / 2} \frac{\sin 2 x}{\left(\sin ^{4} x+\cos ^{4} x\right)} d x$ Solution:...
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Question: Evaluate the following integrals $\int_{0}^{\pi / 2} \frac{\sin x \cos x}{\left(\cos ^{2} x+3 \cos x+2\right)} d x$ Solution:...
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Question: Evaluate the following integrals $\int_{0}^{\pi / 4} \frac{\tan ^{3} x}{(1+\cos 2 x)} d x$ Solution:...
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Question: Evaluate the following integrals $\int_{0}^{\pi} \frac{d x}{(3+2 \sin x+\cos x)}$ Solution:...
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Question: Evaluate the following integrals $\int_{0}^{\pi / 2} \frac{d x}{(\cos x+2 \sin x)}$ Solution:...
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Question: Evaluate the following integrals $\int_{0}^{\pi} \frac{d x}{(5+4 \cos x)}$ Solution:...
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Question: Evaluate the following integrals $\int_{0}^{\pi} \frac{d x}{(6-\cos x)}$ Solution:...
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Question: Evaluate the following integrals $\int_{0}^{\pi / 2} \frac{d x}{(5+4 \sin x)}$ Solution:...
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