List of top Mathematics Questions on Integration by Partial Fractions asked in TS EAMCET

If \[ \frac{x+3}{(1-x)^2(1+x^2)} = \frac{A}{(1-x)} + \frac{B}{(1-x)^2} + \frac{Cx+D}{2(1+x^2)}, \] then \(B^2+C^2+D^2=\)

If \[ \frac{x}{x^{4}+1}=\frac{Ax+B}{f(x)}+\frac{Cx+D}{g(x)}, \quad f(x)g(x)=x^{4}+1, \quad f(1)=2+\sqrt{2}, \] then \[ \frac{1}{D^{3}}+\frac{2}{B}= \]

If \[ \frac{x^{2}+1}{(x^{4}+5x^{2}+6)(x^{6}+x^{4})} = \frac{A}{x^{4}}+\frac{B}{x^{2}}+\frac{C}{x^{2}+2}+\frac{D}{x^{2}+3}, \] then \(A-B=\):

If \[ \frac{2x^{6}+3x^{4}+1}{(x^{2}+2)^{4}}=\frac{Ax+P}{x^{2}+2}+\frac{Bx+Q}{(x^{2}+2)^{2}}+\frac{Cx+R}{(x^{2}+2)^{3}}+\frac{Dx+T}{(x^{2}+2)^{4}}, \] then $3P+2Q+R+4T=$

Evaluate \[ \int \frac{\cos x+\sin2x}{1-\sin x-2\sin^2x}\,dx \]

If \[ \frac{2x^3+x-3}{x^4-5x^2+4} \] then partial fraction form is

If number of circular permutations of 10 distinct things taken 5 at a time is \(m\) and number of linear permutations of 9 distinct things taken 4 at a time is \(n\), then \(m:n=\)

If $\frac{3x+1}{(x-1)^2(x^2+1)} = \frac{A}{x-1} + \frac{B}{(x-1)^2} + \frac{Cx+D}{x^2+1}$, then $2(A-C+B+D)=$

If $\frac{x^2+1}{(x^2+2)(x^2+3)} = \frac{Ax+B}{x^2+2} + \frac{Cx+D}{x^2+3}$, then $A+B+C+D=$

If $\frac{x+3}{(x+1)(x^2+2)} = \frac{a}{x+1} + \frac{bx+c}{x^2+2}$ then $a-b+c =$

If \[ \frac{x^4}{(x^2+1)(x-2)} = f(x) + \frac{Ax+B}{x^2+1} + \frac{C}{x-2} \] then \( f(14) + 2A - B = \) ?

If \[ \frac{3x^4 - 2x^2 +1}{(x-2)^4} = A + \frac{B}{x-2} + \frac{C}{(x-2)^2} + \frac{D}{(x-2)^3} + \frac{E}{(x-2)^4}, \] then \(2A + 3B - C - D + E =\;?\)

If \(\frac{x^2}{2x^2 + 7x + 6} = \frac{Ax + B}{x^2 + a} + \frac{Cx + D}{ax^2 + 3}\), then \(A + B + C - 2D =\)

If $\frac{x^{2} + 5}{\left(x^{2} + 1 \right)\left(x-2\right)} = \frac{A}{x-2} + \frac{Bx+C}{x^{2} + 1 } , $ then $A + B + C = $