Integration by Partial Fractions

$\int \frac{\cos 2x\sin 4xdx}{{\cos }^{4}x\left(1+{\cos }^{2}2x\right)}$

Evaluate $\int \frac{x^2}{x^4-x^2-12}dx$

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

Find: $\int \frac{1}{1+\tan x}dx$

Evaluate the integral and show your steps.

$\int \frac{1}{8-x^3}dx$

Find the value of $\int \frac{dx}{x\log x\left(4+{\left(\log x\right)}^2\right)}$

The general solution of the differential equation $y^{\text{'}}=\frac{4}{x(x-4)}$ is 

Find $\int \frac{x^4}{x^2+1}dx$

Evaluate $\int \frac{dx}{x-x^2}$

FInd the integral value of $\int \frac{3x-1}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}dx$

Find the integral of $\int \frac{x^3}{{\left(x^2-1\right)}^2}dx.$

Find $\int \frac{x^{4}dx}{\left(x-1\right)\left(x^2+1\right)}$

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

Find $\int \frac{\left(3 \sin \varphi -2\right)\cos \varphi }{5-{\cos }^2 \varphi -4 \sin \varphi }d\varphi$

Find $\int \frac{x^2}{\left(x^2+1\right)\left(x^2+4\right)}dx$

Find $\int \frac{3x-2}{{\left(x+1\right)}^2\left(x+3\right)}dx$

Find $\int \frac{x^2+1}{x^2-5x+6}dx$

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

Find $\int \frac{x^4+1}{x^2+1}dx$

Find the integration of $\int \frac{2}{\left(1-x\right)\left(1+x^2\right)}dx.$