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\[\int\limits_0^{\pi/2} \frac{\sin^2 x}{\sin x + \cos x} dx\]
Concept: undefined >> undefined
\[\int\limits_0^{\pi/2} \frac{x}{\sin^2 x + \cos^2 x} dx\]
Concept: undefined >> undefined
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\[\int\limits_{- \pi}^\pi x^{10} \sin^7 x dx\]
Concept: undefined >> undefined
\[\int\limits_0^1 \cot^{- 1} \left( 1 - x + x^2 \right) dx\]
Concept: undefined >> undefined
\[\int\limits_0^\pi \frac{dx}{6 - \cos x}dx\]
Concept: undefined >> undefined
\[\int\limits_0^{\pi/2} \frac{1}{2 \cos x + 4 \sin x} dx\]
Concept: undefined >> undefined
\[\int\limits_{\pi/6}^{\pi/2} \frac{\ cosec x \cot x}{1 + {cosec}^2 x} dx\]
Concept: undefined >> undefined
\[\int\limits_0^{\pi/2} \frac{dx}{4 \cos x + 2 \sin x}dx\]
Concept: undefined >> undefined
\[\int\limits_0^2 \left( 2 x^2 + 3 \right) dx\]
Concept: undefined >> undefined
\[\int\limits_1^4 \left( x^2 + x \right) dx\]
Concept: undefined >> undefined
\[\int\limits_{- 1}^1 e^{2x} dx\]
Concept: undefined >> undefined
\[\int\limits_1^3 \left( 2 x^2 + 5x \right) dx\]
Concept: undefined >> undefined
\[\int\limits_1^3 \left( x^2 + 3x \right) dx\]
Concept: undefined >> undefined
\[\int\limits_0^2 \left( x^2 + 2 \right) dx\]
Concept: undefined >> undefined
\[\int\limits_0^3 \left( x^2 + 1 \right) dx\]
Concept: undefined >> undefined
If \[\vec{a} \text{ and } \vec{b}\] are two non-collinear unit vectors such that \[\left| \vec{a} + \vec{b} \right| = \sqrt{3},\] find \[\left( 2 \vec{a} - 5 \vec{b} \right) \cdot \left( 3 \vec{a} + \vec{b} \right) .\]
Concept: undefined >> undefined
Prove that `int_a^b ƒ ("x") d"x" = int_a^bƒ(a + b - "x") d"x" and "hence evaluate" int_(π/6)^(π/3) (d"x")/(1+sqrt(tan "x")`
Concept: undefined >> undefined
