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Integration Formula

Basic Formula

• $\int kdx = kx+c$
• $\int {x^n} dx = \frac{x^{n+1}}{n+1}+c$
• $\int \frac{1}{x}dx=ln(x)+c$
• $\int e^xdx=c^x+c$
• $\int sinxdx=-cosx+c$
• $\int cosxdx=sinx+c$
• $\int tanxdx=ln(secx)+c$
• $\int cotxdx=ln(sinx)+c$

TrigonMetric Formula

• $\int sin^2xdx=\frac{1}{2}(x-sinxcosx)+c$
• $\int cos^2xdx=\frac{1}{2}(x+sinxcosx)+c$
• $\int sec^2xdx=tanx+c$
• $\int cosec^2xdx=-cotx+c$

Integration by Parts

• $\int udv=uv-\int vdu$
• $\int_a^b udv=[uv]_a^b-\int_a^b vdu$

Integration by Substitution

• $\int f(g(x))g'(x)dx=\int f(u)du$ ; Where $u=g(x)$

Partial Fraction

• $\int \frac{1}{x^2+a^2}dx=\frac{1}{a}tan^{-1}(\frac{x}{a})+c$

• $\int \frac{1}{x^2-a^2}dx=\frac{1}{2a}ln|\frac{x-a}{x+a}|+c$

• $\int \frac{1}{(x-a)(x-b)}dx=\frac{1}{b-a}ln|\frac{x-a}{x-b}|+c$