Let \(I=\int \sqrt{x^2+4x+1}\,dx\)
=\(\int \sqrt{(x^2+4x+4)-3}dx\)
=\(\int \sqrt{(x+2)^2-(\sqrt3)^2}dx\)
It is known that,\(\int \sqrt{x^2-a^2}\,dx=\frac{x}{2}\sqrt{x^2-a^2}-\frac{a^2}{2}\log \mid x+\sqrt{x^2-a^2}\mid+C\)
∴=\(I=\frac{(x+2)}{2}\sqrt{x^2+4x+1-}\frac{3}{2}\log\mid (x+2)+\sqrt{x^2+4x+1}\mid+C\)
Rupal, Shanu and Trisha were partners in a firm sharing profits and losses in the ratio of 4:3:1. Their Balance Sheet as at 31st March, 2024 was as follows:
(i) Trisha's share of profit was entirely taken by Shanu.
(ii) Fixed assets were found to be undervalued by Rs 2,40,000.
(iii) Stock was revalued at Rs 2,00,000.
(iv) Goodwill of the firm was valued at Rs 8,00,000 on Trisha's retirement.
(v) The total capital of the new firm was fixed at Rs 16,00,000 which was adjusted according to the new profit sharing ratio of the partners. For this necessary cash was paid off or brought in by the partners as the case may be.
Prepare Revaluation Account and Partners' Capital Accounts.
There are many important integration formulas which are applied to integrate many other standard integrals. In this article, we will take a look at the integrals of these particular functions and see how they are used in several other standard integrals.
These are tabulated below along with the meaning of each part.