Q.$\left(\sqrt{x}+\dfrac{1}{\sqrt{x}}\right)^2$

Some integrands have no direct standard formula but can be decomposed into a sum or difference of functions whose integrals are known, then integrated term by term. Typical decompositions: expanding a power such as $(3x-1)^2$, splitting a single fraction like $\dfrac{x^2-3x+1}{x}$ into separate terms, and using trigonometric product-to-sum identities (e.g. $2\cos A\sin B=\sin(A+B)-\sin(A-B)$, $\cos^3 x=\tfrac14(3\cos x+\cos 3x)$), power-reduction ($1+\cos 2x=2\cos^2 x$, $1-\cos 2x=2\sin^2 x$), and $\sin^2 x+\cos^2 x=1$.

Partial fractions. When the integrand is a rational function $\dfrac{p(x)}{q(x)}$ with $\deg p<\deg q$ (if not, first do polynomial long division), resolve it into a sum of simpler fractions — one term per distinct linear factor $\dfrac{A}{x-\alpha}$ (and $\dfrac{B}{(x-\alpha)^2}$ for a repeated factor) — determine the constants by comparing coefficients or substituting convenient $x$-values, then integrate each simple fraction (each gives a logarithm or a power).