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If \[\int\frac{1}{5 + 4 \sin x} dx = A \tan^{- 1} \left( B \tan\frac{x}{2} + \frac{4}{3} \right) + C,\] then
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int x^{\sin x} \left( \frac{\sin x}{x} + \cos x . \log x \right) dx\] is equal to
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
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If \[\int\frac{\cos 8x + 1}{\tan 2x - \cot 2x} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
If \[\int\frac{\sin^8 x - \cos^8 x}{1 - 2 \sin^2 x \cos^2 x} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\left( x - 1 \right) e^{- x} dx\] is equal to
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
If `int(2x^(1/2))/(x^2) dx = k . 2^(1/x) + C`, then k is equal to ______.
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{1}{1 + \tan x} dx =\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int e^x \left( 1 - \cot x + \cot^2 x \right) dx =\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{\sin^6 x}{\cos^8 x} dx =\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
If P, Q and R are three collinear points such that \[\overrightarrow{PQ} = \vec{a}\] and \[\overrightarrow{QR} = \vec{b}\]. Find the vector \[\overrightarrow{PR}\].
Chapter: [10] Vectors
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{1}{7 + 5 \cos x} dx =\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{1}{1 - \cos x - \sin x} dx =\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{\sin x}{3 + 4 \cos^2 x} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int e^x \left( \frac{1 - \sin x}{1 - \cos x} \right) dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{2}{\left( e^x + e^{- x} \right)^2} dx\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{e^x \left( 1 + x \right)}{\cos^2 \left( x e^x \right)} dx =\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\frac{\sin^2 x}{\cos^4 x} dx =\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
The primitive of the function \[f\left( x \right) = \left( 1 - \frac{1}{x^2} \right) a^{x + \frac{1}{x}} , a > 0\text{ is}\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int\sqrt{\frac{x}{1 - x}} dx\] is equal to
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
\[\int e^x \left\{ f\left( x \right) + f'\left( x \right) \right\} dx =\]
Chapter: [7] Integrals
Concept: undefined >> undefined
Concept: undefined >> undefined
