evaluate the integral $\int x^3(5x^2+3)^5 dx$ How to evaluate for the integral:
$$\int x^3(5x^2+3)^5 dx$$
What I've tried:
For example,
(1) $u = x^2$ whence $du = 2x$ $dx$
(2)$u = ax^2+b$ whence $du = 2ax$ $dx$ 
Therefore,
(3) $u = 5x^2+3$ whence $du = 10x$ $dx$
$$I = \int \frac{du}{10}u^5 = \frac{1}{10} \int \frac{u^6}{6} du= \frac{1}{10}\frac{1}{6}u^6$$
However, this does not lead me to the answer:
$$\frac{(10x^2-1)(5x^2+3)^6}{700}$$
Where did I go wrong and how do I correct this?

$$\int x^3(5x^2+3)^5 dx=\frac{1}{5}\int(5x^3+3x-3x)(5x^2+3)^5 dx=$$
$$=\frac{(5x^2+3)^7}{5\cdot7\cdot10}-\frac{3(5x^2+3)^6}{5\cdot6\cdot10}+C.$$
