List of top Mathematics Questions on Integration by Partial Fractions asked in MHT CET

\(\int \frac{dx}{(x+2)(x^{2}+1)}\) is equal to
\(\int \frac{x^{3}+x^{2}+2x+1}{x^{2}-x+1}dx=\ldots\)
\(\int \frac{2x}{4-3x-x^{2}}\ dx=\ldots\)
The value of the integral \(\int \frac{dx}{x^{4}+x^{3}}\) is
If \(f(x) = \int \frac{x}{(x^2+4)(x^2+9)}\,dx\) and \(f(0) = \frac{1}{5}log(\frac{2}{3})\), then \(f(1) =\)
If \(\int f(x)\,dx = g(x)\) then \(\int x^3f(x^2)\,dx\) is equal to
\(\int \frac{x^4+1}{x^6+1}dx =\)
\(\int \frac{x^2\,\text{d}x}{(x^2+2)(x^2+5)} =\)
\(\int \frac{(x+1)}{x(1+xe^x)^2}dx =\)
\(\int \frac{sinx}{sin4x}dx =\)
\(\int \frac{2x}{4-3x-x^2}dx = \cdots\)
\(\int \frac{x+2}{x^2-7x+12}dx\) is equal to
Evaluate the integral: \[ \int \frac{2x}{x^2 - 5x + 4}\, dx \]
Evaluate the integral: \[ \int \frac{x+1}{x(1+xe^x)^2}\,dx \]

If \(\int \frac{\left(x^4+1\right)}{x\left(x^2+1\right)^2} d x=A \log |x|+\frac{B}{1+x^2}+c\), then \(\mathrm{A}-\mathrm{B}\) is (where c is the constant of integration)

\(\int \frac{\mathrm{d} x}{x\left(x^3+1\right)}=\)

\[ \int \frac{x^3}{x^4+5 x^2+4} d x= \]

\[ \int \frac{x \mathrm{~d} x}{(x-1)(x-2)}= \]

\[\int \frac{\mathrm{d} x}{2 \mathrm{e}^{2 x}+3 \mathrm{e}^x+1}=\]

\[ \int \frac{\mathrm{d} x}{x\left(x^2+1\right)}= \]

$\int \frac{dx}{x(x^3 + 1)} = \dots$
If $\int \frac{dx}{x^4 + 5x^2 + 4} = A \tan^{-1} x + B \tan^{-1} \frac{x}{2} + c$ where $c$ is a constant of integration, then ______.
If $\int \frac{(x^4+1)}{x(x^2+1)^2} \, dx = A \log |x| + \frac{B}{1+x^2} + c$, then $A - B$ is ______.
Evaluate the integral \[ \int \frac{x^3}{(x+1)^2} \, dx. \]
If \(z = x + iy\) is a complex number, then the equation \(\left| \frac{z+i}{z-i} \right| = \sqrt{3}\) represents the