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Question: Prove that $\int_{0}^{\pi} \frac{x \sin x}{(1+\sin x)} d x=\pi\left(\frac{\pi}{2}-1\right)$ Solution:...
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Question: Prove that $\int_{0}^{\pi} \frac{x \tan x}{(\sec x+\cos x)} d x=\frac{\pi^{2}}{4}$ Solution:...
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Question: Prove that $\int_{0}^{\pi / 2} \frac{\cos ^{2} x}{(\sin x+\cos x)} d x=\frac{1}{\sqrt{2}} \log (\sqrt{2}+1)$ Solution:...
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Question: Prove that $\int_{0}^{\pi} \frac{x \tan x}{(\sec x \operatorname{cosec} x)} d x=\frac{\pi^{2}}{4}$ Solution:...
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Question: Prove that $\int_{0}^{\pi} x \cos ^{2} x d x=\frac{\pi^{2}}{4}$ Solution:...
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Question: Prove that $\int_{0}^{2} x \sqrt{2-x} d x=\frac{16 \sqrt{2}}{15}$ Solution:...
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Question: Prove that $\int_{0}^{1} x(1-x)^{5} d x=\frac{1}{42}$ Solution:...
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Question: Prove that $\int_{0}^{\pi / 2} \frac{(\sin x-\cos x)}{(1+\sin x \cos x)} d x=0$ Solution:...
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Question: Prove that $\int_{0}^{\pi / 2} \frac{\sqrt{\tan x}}{(1+\sqrt{\tan x})} d x=\frac{\pi}{4}$ Solution:...
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Question: Prove that $\int_{0}^{\pi / 2} \frac{\sqrt{\cot x}}{(1+\sqrt{\cot x})} d x=\frac{\pi}{4}$ Solution:...
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Question: Prove that $\int_{0}^{\pi / 2} \frac{d x}{(1+\sqrt{\tan x})}=\frac{\pi}{4}$ Solution:...
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Question: Prove that $\int_{0}^{\pi / 2} \frac{d x}{\left(1+\cot ^{3} x\right)}=\frac{\pi}{4}$ Solution:...
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Question: Prove that $\int_{0}^{\pi / 2} \frac{d x}{\left(1+\tan ^{3} x\right)}=\frac{\pi}{4}$ Solution:...
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Question: Prove that $\int_{0}^{\pi / 2} \frac{\mathrm{dx}}{(1+\cot \mathrm{x})}=\frac{\pi}{4}$ Solution:...
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Question: Prove that $\int_{0}^{\pi / 2} \frac{d x}{(1+\tan x)}=\frac{\pi}{4}$ Solution:...
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Question: Prove that $\int_{0}^{\pi / 2} \frac{\sqrt{\cot x}}{(\sqrt{\tan x}+\sqrt{\cot x})} d x=\frac{\pi}{4}$ Solution:...
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Question: Prove that $\int_{0}^{\pi / 2} \frac{\sqrt{\tan x}}{(\sqrt{\tan x}+\sqrt{\cot x})} d x=\frac{\pi}{4}$ Solution:...
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Question: Prove that $\int_{0}^{\pi / 2} \frac{\sin ^{n} x}{\left(\sin ^{n} x+\cos ^{n} x\right)} d x=\frac{\pi}{4}$ Solution:...
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Question: Prove that $\int_{0}^{\pi / 2} \frac{\sin ^{3 / 2} x}{\left(\sin ^{3 / 2} x+\cos ^{3 / 2} x\right)} d x=\frac{\pi}{4}$ Solution:...
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Question: Prove that $\int_{0}^{\pi / 2} \frac{\cos ^{1 / 4} x}{\left(\sin ^{1 / 4} x+\cos ^{1 / 4} x\right)} d x=\frac{\pi}{4}$ Solution:...
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Question: Prove that $\int_{0}^{\pi / 2} \frac{\cos ^{4} x}{\left(\sin ^{4} x+\cos ^{4} x\right)} d x=\frac{\pi}{4}$ Solution:...
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Question: Prove that $\int_{0}^{\pi / 2} \frac{\cos ^{4} x}{\left(\sin ^{4} x+\cos ^{4} x\right)} d x=\frac{\pi}{4}$ Solution:...
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Question: Prove that $\int_{0}^{\pi / 2} \frac{\sin ^{7} x}{\left(\sin ^{7} x+\cos ^{7} x\right)} d x=\frac{\pi}{4}$ Solution:...
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Question: Prove that $\int_{0}^{\pi / 2} \frac{\cos ^{3} x d x}{\left(\sin ^{3} x+\cos ^{3} x\right)}=\frac{\pi}{4}$ Solution:...
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Question: Prove that $\int_{0}^{\pi / 2} \frac{\sin ^{3} x}{\left(\sin ^{3} x+\cos ^{3} x\right)} d x=\frac{\pi}{4}$ Solution:...
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