Oblicz całkę metodą przez podstawienie: zadania w załączniku

[latex]int frac{ an^7 x}{cos^2 x}dx =[/latex] [latex] an x = t[/latex] [latex]frac{1}{cos^2 x}dx = dt[/latex] [latex]= int t^7 dt = frac{1}{8}t^8 + C = frac{1}{8} an^8 x + C[/latex] [latex]int frac{e^x}{1 + 3e^x}dx =[/latex] [latex]1 + 3e^x = t[/latex] [latex]3e^xdx = dt[/latex] [latex]e^x dx = frac{1}{3}dt[/latex] [latex]= frac{1}{3}int frac{dt}{t} = frac{1}{3}ln|t| + C = frac{1}{3}ln|1 + 3e^x| + C[/latex] [latex]int sqrt{2x + 4} dx =[/latex] [latex]2x + 4 = t[/latex] [latex]2dx = dt[/latex] [latex]dx = frac{1}{2}dt[/latex] [latex]= frac{1}{2} int sqrt{t} dt = frac{1}{2} cdot frac{2}{3}sqrt{t^3} + C = frac{1}{3}sqrt{(2x + 4)^3} + C[/latex] [latex]int 3xsqrt{1 - x^2}dx = 3int xsqrt{1 - x^2}dx =[/latex] [latex]1 - x^2 = t[/latex] [latex]-2xdx = dt[/latex] [latex]xdx = -frac{1}{2}dt[/latex] [latex]= 3 cdot (-frac{1}{2})int sqrt{t} dt = -frac{3}{2} cdot frac{2}{3}sqrt{t^3} + C = -sqrt{(1 - x^2)^3} + C[/latex]