Indefinite Integral

In calculus, an indefinite integral (also an antiderivative, inverse derivative, primitive function or primitive integral) of a function f is a differentiable function F whose derivative is equal to the original function f. Solving indefinite integral is opposite operation to differentiation.


$$f(x)={F}'x, \textrm{then}$$ $$\int f(x)dx=Fx+C.$$

Multiplication by constant

$$\int c \times f(x)dx=c \times \int f(x)dx$$

Sum and difference

$$\int [f(x)\pm g(x)] dx=\int f(x)dx \pm \int g(x) dx$$

Integration by parts

$$\int u dv=uv-\int vdu, \;\textrm {where}$$ $$u=u(x)\; \textrm {ja} \;v=v(x)$$

Substitution rule

$$\int f(x)dx=\int f(g(t)){g}'(t)dt, \;\textrm{where}$$ $$x=g(t)$$

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