• Such problems require the use of method of substitution along with method of integration by parts.
By method of integration by parts if we have :
∫ f(x)g(x)dx = f(x) ∫ g(x)dx - ∫ f'(x)(∫ g(x)dx) dx
• To solve the integrals of the form :
\(\int\sqrt{ax^2+bx+c}\)
After applying substitution and integration by parts we have direct formulae as described below :
Let I = ∫1/x√(16+(logx)2)dx
Let log x = t
Differentiating both sides:
⇒ \(\frac{1}{x}\) dx = dt
Substituting (log x) with t,
We have:
