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Formulas

Integrals

Showing formulas of Integrals

Math
Subject
Calculus
Sub Subject
Showing 9 of 9 formulas Page 1 of 1

Integration by Parts

Math → Calculus → Integrals → Integration Techniques
$$\int u \, dv = uv - \int v \, du$$
A rule that transforms the integral of a product of functions into other forms.
📖 Math 📚 Integrals

Integration of Exponential Function

Math → Calculus → Integrals → Basic Integration
$$\int e^{ax} \, dx = \frac{1}{a} e^{ax} + C$$
The integral of the natural exponential function with a linear exponent constant.
📖 Math 📚 Integrals

Integration of a Constant

Math → Calculus → Integrals → Basic Integration
$$\int k \, dx = kx + C$$
The antiderivative of a constant value.
📖 Math 📚 Integrals

Integration of 1/x

Math → Calculus → Integrals → Basic Integrals
$$\int \frac{1}{x} \, dx = \ln|x| + C$$
Special case for integrating power functions where $n = -1$.
📖 Math 📚 Integrals

Integration of Secant Squared

Math → Calculus → Integrals → Trigonometric Integration
$$\int \sec^2 x \, dx = \tan x + C$$
The standard integral for the square of the secant function.
📖 Math 📚 Integrals

Integration of $1/\sqrt{a^2 - x^2}$

Math → Calculus → Integrals → Inverse Trig Integrals
$$\int \frac{dx}{\sqrt{a^2 - x^2}} = \sin^{-1}\left(\frac{x}{a}\right) + C$$
Standard integral result involving inverse sine.
📖 Math 📚 Integrals

Integration of Logarithm

Math → Calculus → Integrals → Integration Techniques
$$\int \ln x \, dx = x \ln x - x + C$$
The antiderivative of the natural logarithm function.
📖 Math 📚 Integrals

Integration of $1/(x^2 + a^2)$

Math → Calculus → Integrals → Integration Formulas
$$\int \frac{dx}{x^2 + a^2} = \frac{1}{a} \tan^{-1}\left(\frac{x}{a}\right) + C$$
Standard integral leading to the inverse tangent function.
📖 Math 📚 Integrals

Integration of $a^x$

Math → Calculus → Integrals → Exponential Integration
$$\int a^x \, dx = \frac{a^x}{\ln a} + C$$
The general integral for exponential functions where the base is any positive constant.
📖 Math 📚 Integrals
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