Integration Using Partial Fractions

If $\int \frac{x+3}{{\left(x-1\right)}^2\left(2x-1\right)}dx=\frac{\mathrm{A}}{x-1}+B \log \left(2\mathrm{x}-1\right)+C \log \left(\mathrm{x}-1\right)+K$ then $A+B+C=$

$\int \frac{x^5+1}{x+1}dx=$_____$+C$

Evaluate $\int \frac{(2x+9)}{(x+2)(x-3{)}^2}dx$.

Evaluate the following: 

$\int \frac{x^2+x-1}{x^2+x-6}dx$

Evaluate ${\int }_2^3\frac{x}{\left(x+2\right)\left(x+3\right)}dx$.

Evaluate${\int }_1^2\frac{dx}{x^2+6x+5}$

Integrate the following function with respect to $\mathrm{x}$

$\frac{1}{\left(1+e^x\right)\left(1-e^{-x}\right)}$

Integrate the following function with respect to $x$

 $\frac{3\mathrm{x}-2}{(\mathrm{x}+1{)}^2(\mathrm{x}+3)}$

Integrate the following function with respect to $x$

 $\frac{3\mathrm{x}}{(\mathrm{x}+1)(\mathrm{x}-2)}$ 

Integrate the following function with respect to $x$

$\frac{{\mathrm{x}}^2}{(\mathrm{x}+1)(\mathrm{x}-2)(\mathrm{x}-3)}$

Evaluate the following :

$\int \frac{(3\sin x-2)\cos x}{5-{\cos }^{2}x-4\sin x}dx$

Evaluate the following :

$\int \frac{x}{(x-1)\left(x^2+1\right)}dx$

Evaluate the following :

$\int \frac{5x^2+20x+6}{x^3+2x^2+x}dx$

Evaluate the following :

Evaluate the following :

Evaluate the following :

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

Evaluate the following :

$\int \frac{2x+7}{(x-4{)}^2}dx$

Integrate the following function w.r. to $x$:

$\frac{1}{\sin \theta (3+2\cos \theta )}$

Integrate the following function w.r.t. $x$:

$\frac{1}{\cos y+\sin 2y}$

Integrate the following function w.r. to $x$:

$\frac{1}{\sin \theta +\sin 2\theta }$