# Integral calculus - Indefinite integral

1. $\int f(x)dx=F(x)+C \ \ if \ \ F' (x) = f(x).$
2. $(\int f(x)dx )'=f(x)$
3. $\int kf (x) dx = k \int f(x) dx$
4. $\int [f(x)+g(x)]dx= \int f(x)dx+ \int g(x)dx$
5. $\int [f(x)-g(x)]dx= \int f(x)dx- \int g(x)dx$
6. $\int [f(ax)dx= {1 \over a} F(ax)+C$
7. $\int f(ax+b)dx= {1 \over a}F (ax+b ) +C$
8. $\int f(x)f'(x)dx={1 \over 2}f^2(x)+c$
9. $\int {\text {f'(x)} \over f(x)}dx |= In | f(x) |+C$
10. Method of substitution
$\int f(x)dx= \int f(u(t))u'(t)dt\:\: \:if \:=x=u(t).$
11. Integration by Parts
$\int udv=uv- \int vdu,$
Where u(x), v(x) are differentiable functions.