# Math Help - Calculus help please!!!

I don't even know where to start on these... please show steps so I can try to learn this stuff...

1. ∫ x ²(x ³+3)^9 dx

2.
∫ x
------- *dx
(x
² +7)^5

3. sec(x)^15 tan(x) dx

Thank you so much!

2. 2 came out wrong, its: x / (x^2 + 7)^5

3. 1. $\int x^2 (x^3+9)^9 dx$. Use substitution, $u=x^3+9$. So $du = 3x^2dx, dx = \frac{du}{3x^2}$ and resubstituting back in,

$\int x^2 (x^3+9)^9 dx=\frac{1}{3}\int u^9du=\frac{u^{10}}{30}+C=\frac{(x^3+9)^{10}}{30}+ C.$

2. $\int \frac{x}{(x^2+7)^5}dx$. Substitute $u=x^2+7$.

3. $\int \sec^{15} x \tan x\;dx$. Substitute $u = \sec x$.