How to Integrate sin^5x | Integral of sin^5x

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

Integral of natural log of x: Formula, Proof

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

Integral of cosec square x | Cosec^2x Integration

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

Integral of 1/x^n (1 by x power n): Formula, Proof

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

How to Integrate Square Root cotx | Find ∫√cotx dx

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

How to Integrate sin^3x cos^2x | Integration of sin^3x cos^2x

The integration of sin^3x cos^2x is equal to (cos5x)/5 – (cos3x)/3 +C where C is a constant. Here we learn how to integrate sin^3x cos^2x. What is the Integration of sin3x cos2x? Question: Find the integral of sin3x cos2x, that is, Find ∫sin3x cos2x dx Solution: We have: ∫sin3x cos2x dx = ∫sin2x sin x … Read more

What is the Integration of coshx? | Integral of coshx

The integration of coshx is equal to sinhx+C. Here we learn how to integrate coshx, the cosine hyperbolic function. The integration formula of cosh(x) is given as follows: ∫coshx dx = sinhx +C where C denotes an integral constant. How to Integrate coshx Question: What is the integral of coshx? That is, Find ∫coshx dx. … Read more