The integration of sin square x is equal to x/2 – (sin2x)/4 +C. Here we learn how to integrate sin2x. The integration of sin2x formula is given by ∫sin2x dx = x/2 – (sin2x)/4 +C where C is an arbitrary integral constant. How to Integrate sin^2x To integrate sin square x, we will use the … Read more
The integration of fourth root of x is 4×5/4/5 + C. In this post, we will find the integral of the fourth root of x by the power rule of integration. Let us now learn how to integrate fourth root x. Integral of Fourth Root of x The fourth root of x is expressed as … Read more
The integration of sin cube x is equal to -cosx + cos3x/3+C where C denotes an integral constant. In this post, we will learn how to integrate sin^3x. Sine cube x integration formula: The integration formula of sin3x is given by What is the integral of sin^3x Answer: The integral of sin^3x is equal to … Read more
The integral of sinxcosx is equal to -(cos2x)/4+C or, (sin2x)/2+C where C is an integration constant. In this post, we will learn how to integrate sinx cosx. The integration formula of sinxcosx is give as follows: Find the integration of sinx cosx Answer: The integration of sinx cosx is (sin2x)/2+C. proof: There are three methods … Read more
The integration of x/(1+x), that is, the integral of x divided by 1+x is equal to x – ln|1+x|+C. In this post, we will learn how to integrate x/(1+x). To find the integral $\int \dfrac{x}{1+x} dx$, we will use the following power rule of the integration formula: ∫dx/x =ln|x|+C …(I) Integration of x/(1+x) Question: Find … Read more
The integration of x/(1+x^2), that is, the integral of x divided by 1+x2 is equal to 1/2 ln(1+x2) + C, where C is a constant. Here ln denotes the natural logarithm. In this post, we will learn how to integrate x divided by 1+x^2. Let’s find the integral: $\int \dfrac{x}{1+x^2} dx$. To find the above … Read more
The integration of the square root of 1+sin2x is given by ∫√(1+sin2x) dx = cosx-sinx+C where C is an integration constant. In this post, we will learn how to integrate square root of 1+sin2x. Integral of Square Root of 1+sin2x Question: Find the integral of 1+sin2x, that is, find ∫√(1+sin2x) dx. Answer: We will use … Read more
The integration of e to the x2 is equal to $\dfrac{\sqrt{\pi}}{2}$ erfi(x)+C, where erfi(x) is called the “imaginary error function” and C is an integration constant. In this post, we will learn to integrate the function $e^{x^2}$. Integral of $e^{x^2}$ We know that ex can be written as ex = $\sum_{n=0}^\infty \dfrac{x^n}{n!}$ = $1+x+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+\cdots +$ … Read more
The integration of e2x is equal to e2x/2. In this post, we will learn how to integrate e to the 2x. The integration of e2x can be derived directly from the formula of the integral of emx which is given below: $\int e^{mx} dx=\dfrac{e^{mx}}{m}+C$ where C is an integration constant. Putting m=2 in the above … Read more
The integration of xn is given as follows: ∫xndx = xn+1/(n+1) + C where C is an integration constant. In this post, we will learn how to find the integral of x to the power n. Integration of xn Formula The integration formula of xn (n-th power x) is given below: ∫xndx = xn+1/(n+1) + … Read more