Porisma

A hint to get started

Complete the square and match a standard integral

Find the following integrals:

(a) ∫12−9x2 dx\displaystyle\int \dfrac1{2-9x^2}\,dx

(b) ∫16+4y−y2 dy\displaystyle\int \dfrac1{6+4y-y^2}\,dy

(c) ∫1y2−4y−13 dy\displaystyle\int \dfrac1{y^2-4y-13}\,dy

(d) ∫12y2−4y−1 dy\displaystyle\int \dfrac1{2y^2-4y-1}\,dy

(e) ∫1x2+4x+20 dx\displaystyle\int \dfrac1{x^2+4x+20}\,dx

(f) ∫12x2+3x+10 dx\displaystyle\int \dfrac1{2x^2+3x+10}\,dx

(g) ∫15−4y−y2 dy\displaystyle\int \dfrac1{\sqrt{5-4y-y^2}}\,dy

(h) ∫125−9x2 dx\displaystyle\int \dfrac1{\sqrt{25-9x^2}}\,dx.

CJC · Discussion · Question 4

Complete the square before choosing between logarithm, arctangent and inverse sine.

Read the worked solution