Buzztutor Questions and Answers by Category

5189

Mathematics Integration Level: Misc Level

Special type

$\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c$

Integrate the following

$\int [Sin(logx)+Cos(log(x))]dx$

5188

Mathematics Integration Level: Misc Level

Special type

$\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c$

Integrate the following

$\int (Cosx+3Sinx)e^{3x}dx$

5187

Mathematics Integration Level: Misc Level

Special type

$\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c$

Integrate the following

$\int \frac{2+Sin2x}{1+Cos2x}e^{x}dx$

5186

Mathematics Integration Level: Misc Level

Special type

$\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c$

Integrate the following

$\int \frac{xe^{2x}}{(1+2x)^{2}}dx$

5185

Mathematics Integration Level: Misc Level

Special type

$\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c$

Integrate the following

$\int \frac{x-1}{(x+1)^{3}}e^{x}dx$

5184

Mathematics Integration Level: Misc Level

Special type

$\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c$

Integrate the following

$\int e^{x}(Cotx+log|Sinx|)dx$

5183

Mathematics Integration Level: Misc Level

Special type

$\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c$

Integrate the following

$\int \frac{2x-1}{4x^{2}}e^{2x}dx$

5182

Mathematics Integration Level: Misc Level

Special type

$\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c$

If $\int \frac{x-1}{x^{2}}e^{x}dx=f(x)e^{x}+c$ then find f(x)

5181

Mathematics Integration Level: Misc Level

Special type

$\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c$

Integrate the following

$\int (x+1)e^{x}dx$

5180

Mathematics Integration Level: Misc Level

Special type

$\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c$

Integrate the following

$\int e^{x}(Cotx+Cosec^{2}x)dx$

5179

Mathematics Integration Level: Misc Level

Special type

$\int e^{x}(f(x)+f'(x))dx=e^{x}f(x)+c$

Integrate the following

$\int e^{x}(tanx+Sec^{2}x)dx$

5178

Mathematics Integration Level: Misc Level

Special type

Rule to evaluate

$\int \frac{x^{2}+A}{x^{4}+kx^{2}+A^{2}}dx, A>0$ or $\int \frac{x^{2}-A}{x^{4}+kx^{2}+A^{2}}dx, A<0$

Where k is a real number (positive, negative or zero)

(i) Divide the numerator and denominator by x²

(ii) For x² + A in the numerator put x - A/x =t as substitution . And for x² - A in the numerator, put x + A/x = t

$\int \sqrt{Cotx}dx$

5177

Mathematics Integration Level: Misc Level

Special type

Rule to evaluate

$\int \frac{x^{2}+A}{x^{4}+kx^{2}+A^{2}}dx, A>0$ or $\int \frac{x^{2}-A}{x^{4}+kx^{2}+A^{2}}dx, A<0$

Where k is a real number (positive, negative or zero)

(i) Divide the numerator and denominator by x²

(ii) For x² + A in the numerator put x - A/x =t as substitution . And for x² - A in the numerator, put x + A/x = t

$\int \frac{x^{2}-3x+1}{x^{4}-x^{2}+1}dx$

5176

Mathematics Integration Level: Misc Level

Special type

Rule to evaluate

$\int \frac{x^{2}+A}{x^{4}+kx^{2}+A^{2}}dx, A>0$ or $\int \frac{x^{2}-A}{x^{4}+kx^{2}+A^{2}}dx, A<0$

Where k is a real number (positive, negative or zero)

(i) Divide the numerator and denominator by x²

(ii) For x² + A in the numerator put x - A/x =t as substitution . And for x² - A in the numerator, put x + A/x = t

$\int \frac{x^{2}}{x^{4}+1}dx = I$

5175

Mathematics Integration Level: Misc Level

Special type

Rule to evaluate

$\int \frac{x^{2}+A}{x^{4}+kx^{2}+A^{2}}dx, A>0$ or $\int \frac{x^{2}-A}{x^{4}+kx^{2}+A^{2}}dx, A<0$

Where k is a real number (positive, negative or zero)

(i) Divide the numerator and denominator by x²

(ii) For x² + A in the numerator put x - A/x =t as substitution . And for x² - A in the numerator, put x + A/x = t

$\int \frac{x^{2}+4}{x^{4}+kx^{2}+16}dx$

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