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Karnataka Board PUCPUC Science 2nd PUC Class 12

PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions

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Evaluate the following integrals: 

`int "sec x"/"sec 2x" "dx"`
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{\cos 2x}{\left( \cos x + \sin x \right)^2} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

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\[\int\frac{1 + \tan x}{1 - \tan x} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{1}{x \log x} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{1}{e^x + 1} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
` ∫ {cot x}/ { log sin x} dx `
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{e^{2x}}{e^{2x} - 2} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{2 \cos x - 3 \sin x}{6 \cos x + 4 \sin x} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{\cos 2x + x + 1}{x^2 + \sin 2x + 2x} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{1}{\cos\left( x + a \right) \cos\left( x + b \right)}dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{sec x}{\log \left( \text{sec x }+ \text{tan x} \right)} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{{cosec}^2 x}{1 + \cot x} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{10 x^9 + {10}^x \log_e 10}{{10}^x + x^{10}} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{1}{\sqrt{x}\left( \sqrt{x} + 1 \right)} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{e^{x - 1} + x^{e - 1}}{e^x + x^e} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{1}{\sin x \cos^2 x} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{1}{\cos 3x - \cos x} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
\[\int\frac{e^x}{\left( 1 + e^x \right)^2} dx\]
[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

 ` ∫       cot^3   x  "cosec"^2   x   dx `

[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined

\[\int\frac{\left\{ e^{\sin^{- 1} }x \right\}^2}{\sqrt{1 - x^2}} dx\]

[7] Integrals
Chapter: [7] Integrals
Concept: undefined >> undefined
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