If $\int {({x^3} - 2{x^2} + 5){e^{3x}}\,dx} = e^{3x} (Ax^3 + Bx^2 + Cx + D) + K$,then the statement which is incorrect is

$\int \frac{d x}{4 \sin x+3 \cos x}=$

If $\int \frac{1+\cos 8 x}{\tan 2 x-\cot 2 x} d x=f(x) \cdot \cos (g(x))+c$, then $f\left(\frac{1}{4}\right)+g\left(\frac{1}{4}\right)=$

Given that $\int_0^\infty \frac{x^2 \, dx}{(x^2 + a^2)(x^2 + b^2)(x^2 + c^2)} = \frac{\pi}{2(a + b)(b + c)(c + a)}$,then the value of $\int_0^\infty \frac{x^2 \, dx}{(x^2 + 4)(x^2 + 9)}$ is

If $I_n = \int \frac{\sin nx}{\cos x} dx$,then $I_n =$

If $I=\int \frac{\sin x+\sin ^3 x}{\cos 2 x} \,d x=P \cos x+Q \log \left|\frac{\sqrt{2} \cos x-1}{\sqrt{2} \cos x+1}\right|+c,$ (where $c$ is a constant of integration),then the values of $P$ and $Q$ are respectively