The integration of cosec x is ln|cosec x-cot x|. Here ln stands for the natural logarithm, that is, ln x = logex. In this post, we will learn how to integrate cosec x. Integration of Cosecx Formula Cosecx integration formula: The integration formula of cosec x is given below. ∫cosecx dx = ln|cosecx-cotx|+C where C … Read more
The integration of secx is equal to ln|secx+tanx| where ln denotes the natural logarithm, that is, the logarithm with base e. In this post, we will learn how to find the integral of secx dx. Integration of Secx Formula The sec x integration formula is given below. ∫secx dx = ln|secx+tanx|+C Integration of Secx Proof … Read more
The integration of cotx is ln|sinx|, where ln denotes the natural logarithm, that is, the logarithm with base e. Here we will learn how to find the integral of cotx dx. cotx Integration Formula The cotx integration formula is given below. ∫cotx dx = ln|sinx|+C Integration of cotx Proof We will show that ∫cotx dx … Read more
The integration of tanx is -ln|cosx| or ln|secx|, where ln denotes the natural logarithm, that is, logarithm with base e. Here we will learn how to find the integral of tanx dx. tanx Integration Formula The tanx integration formula is given below. Integration of tanx Proof We will show that ∫tanx dx = -ln|cosx|+C. As … Read more
The integration of the square root of a2+x2 is given as follows: $\int \sqrt{a^2+x^2} dx$ $=\dfrac{x}{2} \sqrt{a^2+x^2}$ $+\dfrac{a^2}{2}\log |x+\sqrt{a^2+x^2}|+C$, where $C$ is an integration constant. In this post, we will find the integral of root(a2+x2). Let’s learn how to integrate square root of a2+x2. Integration of $\sqrt{a^2+x^2}$ Question: What is the integration of square root … Read more
The integration of tan^2x is equal to ∫tan2x dx = tan (x)-x. In this post, we will learn how to find the integral of tan square x. We will use the following two formulas: Integration of tan2x Question: What is the integration of tan2 x? That is, find ∫tan2 x dx. Answer: ∫tan2x dx = … Read more
In this post, we will find the integral of root(a2-x2). The integration of square root of a2-x2 is given as follows ∫ √(a2-x2) dx = x/2 ⋅ √(a2-x2) + a2/2 sin-1(x/a) + C, where C is an integration constant. Integration of $\sqrt{a^2-x^2}$ Let $I = \int \sqrt{a^2-x^2} dx$ $\cdots (I)$ We will find the integration … Read more
The integration of 1/(1+x2) is equal to tan2 x. In this post, we will see how to integrate 1/(1+x^2). Integration of $\dfrac{1}{1+x^2}$ Question: What is the integration of $\dfrac{1}{1+x^2}$? That is, Find $\int \dfrac{1}{1+x^2} dx$ Answer: The integration of $\dfrac{1}{1+x^2}$ is $\tan^2 x$. Explanation: Let us substitute $x=\tan t$ $\cdots (\star)$ Differentiating with respect to … Read more
The integration of e3x is e3x/3. In this post, we will learn how to find the integral of e to the 3x. Let us recall the formula of the integral of emx: $\int e^{mx} dx=\dfrac{e^{mx}}{m}+C$ where C is an integral constant. Thus, the integral of e3x will be equal to $\int e^{3x} dx=\dfrac{e^{3x}}{3}+C$. What is the … Read more
The derivative of 1 by root x is -1/(2x root(x)). In this post, we will find the derivative of 1/root(x) by the first principle of derivatives. We will also find the integration of 1 by root x. Derivative of 1 by root x from First Principle The first principle of derivatives says that the derivative … Read more