The integral of ln2x is equal to x(ln2x−1)+C where C is a constant. Here, we will learn how to integrate ln2x. The integration of ln(2x) is given as follows: ∫ln2x dx = x(ln2x−1)+C Integration of ln2x Question: What is the integration of ln2x? Solution: To find the integration of ln2x, we will use the integration … Read more
The integral of e^(-x) from 0 to infinity is equal to 1. Here we will learn how to integrate e-x (e to the power -x) from 0 to ∞. Answer: The integral of e-x from 0 to infinity is equal to 1. That is, $\int_0^\infty e^{-x} dx =1$. Explanation: The integration of e-x from 0 … Read more
The integral of sin^5x is equal to ∫sin5x dx = -(cos5x)/5 + (2cos3x)/3 -cos x+C, where C denotes an integration constant. Here we will learn how to integrate sin^5x. The integration formula of sin5x is given by $\int \sin^5x$ $=-\dfrac{\cos^5x}{5}+\dfrac{2}{3} \cos^3x -\cos x +C$ where C is a constant. Integration of sin5x Question: Find the … Read more
The natural log of x is the logarithm of x with base e, and it is denoted by ln(x). That is, logex = lnx. The integral of natural log of x is equal to ∫ln(x) dx = xln(x) -x+C, where C is a constant. Here, we will learn how to find the integration of natural … Read more
The integral of cosec square x is equal to -cot(x)+C where C is a constant. In this post, we will learn how to integrate cosec^2x. The integration formula of cosec^2x is given as follows: ∫cosec2x dx = -cotx+C What is the Integration of cosec^2x Answer: The integration of cosec2x is -cotx+C. Proof: First, recall the … Read more
The integral of 1/x^n (1 by x power n) is equal to x-n+1/(1-n) +C. Here we will learn how to integrate 1/xn using the power rule of integration. The integration formula of 1/xn is given by $\int \dfrac{dx}{x^n}=\dfrac{x^{1-n}}{1-n}+C$ where C denotes an integral constant. Integration of 1/xn The integral of 1/xn is denoted by ∫dx/xn. … Read more
The integral of root cotx is equal to ∫√cotx dx = $-\dfrac{1}{\sqrt{2}}$ tan-1 ($\dfrac{\cot x-1}{\sqrt{2\cot x}}$) – $\dfrac{1}{2\sqrt{2}}$ log $|\dfrac{\cot x+1-\sqrt{2\cot x}}{\cot x+1+\sqrt{2\cot x}}|$ +C where C is an arbitrary integral constant. Here we will learn how to integrate square root of cotx. Integral of √cotx Question: Find ∫√cotx dx. Solution: Let cotx=t2. Differentiating w.r.t … Read more
The integration of root tanx + root cotx is equal to √2sin-1(sinx−cosx)+C. Here we learn how to integrate √tanx+√cotx. The integral formula of $\sqrt{\tan x}+\sqrt{\cot x}$ is given by $\int (\sqrt{\tan x}+\sqrt{\cot x}) dx$ = $\sqrt{2}\sin^{-1}(\sin x -\cos x)+C$. Find ∫(√tanx+√cotx) dx $\int (\sqrt{\tan x}+\sqrt{\cot x}) dx$ = $\int \Big(\dfrac{\sqrt{\sin x}}{\sqrt{\cos x}}+\dfrac{\sqrt{\cos x}}{\sqrt{\sin x}} \Big) … Read more
The integral of $\sqrt{1-x^2}$ is equal to $\dfrac{x}{2} \sqrt{1-x^2}$ $+\dfrac{1}{2}$ sin-1 x+C. Here we will learn how to integrate square root of 1-x2. The integral formula of root 1-x^2 is provided below:$\int \sqrt{1-x^2} dx$ $=\dfrac{x}{2} \sqrt{1-x^2}$ $+\dfrac{1}{2}$ sin-1 x+C. Integration of $\sqrt{1-x^2}$ Question: How to Integrate Root (1-x^2)? That is, find $\int \sqrt{1-x^2} dx$. Solution: … Read more
The integral of root tanx is equal to ∫√tanx dx = $\dfrac{1}{\sqrt{2}}$ tan-1 ($\dfrac{\tan x-1}{\sqrt{2\tan x}}$) + $\dfrac{1}{2\sqrt{2}}$ log $|\dfrac{\tan x+1-\sqrt{2\tan x}}{\tan x+1+\sqrt{2\tan x}}|$ +C where C denotes an integral constant. In this post, we will learn how to find the integral of square root of tanx. Integration of √tanx Question: Find ∫√tanx dx. Solution: … Read more