Indefinite Integration

What is $\int \frac{d x}{\sec x+\tan x}$ equal to ?

What is $\int e^{\left(2 \ln x+\ln x^2\right)} d x$ equal to?

If $p(x)=(4 e)^{2 x}$, then what is $\int p(x) d x$ equal to?

What is $\int \frac{d x}{x\left(x^n+1\right)}$ equal to?

What is $\int \frac{d x}{\sec ^2\left(\tan ^{-1} x\right)}$ equal to ?

What is the integral of $f(x)=1+x^2+x^4$ with respect to $x^2 ?$

What is $\int e^{x \ln (a)} d x$ equal to ?

What is $\int \frac{d x}{2 x^2-2 x+1}$ equal to?

What is $\int(\sin x)^{-1 / 2}(\cos x)^{-3 / 2} d x$ equal to?

What is $\int \frac{d x}{x(1+\ln x)^n}$ equal to $\left(n^1 1\right)$ ?

Paragraph: Let $f(x)=P e^x+Q e^{2 x}+R e^{3 x}$, where $P, Q, R$ are real numbers. Further $f(0)=6, f^{\prime}(\ln 3)=282$ and $\int_0^{\ln 2} f(x) d x=11$ Question: What is the value of Q ?

What is $\int e^{\mathrm{x}}(1+\ln x+x \ln x) d x$ equal to?