$$\int \frac{\sin x}{3+4 \cos ^2 x} d x$$

$$\int \frac{1}{x\left[6(\log x)^2+7 \log x+2\right]} d x \text { is }$$

$\int \frac{\sin \frac{3 x}{2}}{\sin \frac{x}{2}} d x$ is

$$\int \sqrt{\operatorname{cosec} x-\sin x} d x$$ is equals to

$$\int \sqrt{5-2 x+x^2} d x$$ is equals to

$$\int \frac{1}{1+3 \sin ^2 x+8 \cos ^2 x} d x$$ is equals to

$$\int \frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha} d x$$ is equal to

If $$\int \frac{d x}{(x+2)\left(x^2+1\right)}=a \log \left|1+x^2\right|+b \tan ^{-1} x +\frac{1}{5} \log |x+2|+c,$$ then

$$\int \frac{x^3 \sin \left(\tan ^{-1}\left(x^4\right)\right)}{1+x^8} d x$$ is equal to

The value of $$\int \frac{x^2 d x}{\sqrt{x^6+a^6}}$$ is equal to

The value of $$\int \frac{x e^x d x}{(1+x)^2}$$ is equal to

The value of $$\int e^x\left[\frac{1+\sin x}{1+\cos x}\right] d x$$ is equal to

The value of $$\int \frac{1+x^4}{1+x^6} d x$$ is

The value of $$\int e^{\sin x} \sin 2 x d x$$ is

If $$\int \frac{3 x+1}{(x-1)(x-2)(x-3)} d x A \log |x-1| B \log |x-2|+C \log |x-3|+C$$, then the values of $$A, B$$ and $$C$$ are respectively

$$\int x^3 \sin 3 x d x=$$

$$\int \frac{1}{\sqrt{x}+x \sqrt{x}} d x=$$

$$\begin{aligned} & \int \frac{2 x-1}{(x-1)(x+2)(x-3)} d x \\ & \quad=A \log |x-1|+B \log |x+2|+C \log |x-3|+K \end{aligned}$$

Then $$A, B, C$$ are respectively

$$ \int \sqrt{x^2+2 x+5} d x \text { is equal to } $$