# Thread: intergrating

1. ## intergrating

please can anyone solve the following problems for me and show me step by step working please

1)integral(x^2 (e^5)^x, dx)

2)[IMG]file:///C:/Users/Taichi/AppData/Local/Temp/moz-screenshot-2.jpg[/IMG]integral(4 x/sqrt(8 x^2-1), dx, 1, 2)

3)integral((x^3-2 x^2-4 x-4)/(x^2+x-2), x)

Thanks in advance

Tiachi[IMG]file:///C:/Users/Taichi/AppData/Local/Temp/moz-screenshot-1.jpg[/IMG]

2. Originally Posted by taichi2910
please can anyone solve the following problems for me and show me step by step working please

1)integral(x^2 (e^5)^x, dx)

2)[IMG]file:///C:/Users/Taichi/AppData/Local/Temp/moz-screenshot-2.jpg[/IMG]integral(4 x/sqrt(8 x^2-1), dx, 1, 2)

3)integral((x^3-2 x^2-4 x-4)/(x^2+x-2), x)

Thanks in advance

Tiachi[IMG]file:///C:/Users/Taichi/AppData/Local/Temp/moz-screenshot-1.jpg[/IMG]
Sorry but we don't give any step by step solutions unless you've shown you've attempted them.

1) Notice that $\displaystyle (e^5)^x = e^{5x}$.

So the integral becomes $\displaystyle \int{x^2e^{5x}\,dx}$.

Use Integration by Parts.

2) Rewrite as $\displaystyle \int_1^2{4x(8x^2 -1)^{-\frac{1}{2}}\,dx}$

Use a u-substitution with $\displaystyle u = 8x^2 - 1$.

3) Long divide first.