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
The integration of root x + 1/root x is equal to 2/3 x3/2+2√x+C where C is an integral constant. In this post, we will learn how to integrate √x+1/√x. Integral of √x+1/√x Question: Find $\int (\sqrt{x}+\dfrac{1}{\sqrt{x}})\ dx$ Answer: $\int (\sqrt{x}+\dfrac{1}{\sqrt{x}})\ dx$ = $\int \sqrt{x}\ dx$ + $\int \dfrac{1}{\sqrt{x}}\ dx$ by the sum rule of integration. … Read more
The integration of ln x is equal to xln x -x+C where C is an integral constant. Ln x denotes the natural logarithm of x, that is, ln x=logex. The integration of lnx is denoted by the symbol ∫ln(x) dx. In this post, we will learn how to integrate ln x. The formula of the … Read more
The integration of (ax+b)/(cx+d) is equal to ax/c + (bc-ad)/c2 ln|cx+d|+K where K is an integral constant and ln denotes the natural logarithm. In this post, we will learn how to integrate the function (ax+b)/(cx+d). Integration of (ax+b)/(cx+d) Formula The integration of (ax+b)/(cx+d) formula is given below. $\int \dfrac{ax+b}{cx+d} \ dx$ $=\dfrac{ax}{c} + \dfrac{bc-ad}{c^2} \ln|cx+d|+K$, … Read more
The integration of 1/x is equal to ln|x|+C where ln denotes the natural logarithm, that is, ln|x|=loge|x| and C is the integration constant. In this post, we will learn how to integrate 1/x. Integration of 1/x Formula The formula for the integration of 1/x (1 divided by x) is given below. ∫ 1/x dx = … Read more
The integration of 2x is equal to 2x/ln2 where ln denotes the natural logarithm, that is, ln=loge. In this post, we will learn to integrate 2 to the power x with respect to x. Integration of 2x Formula The integration formula of 2x (2 to the x) with respect to x is given below. ∫ … Read more
The integration of 1/(1+x2) is tan-1x+C. In this post, we will learn how to integrate 1 divided by 1 plus x square by the substitution method. Integration of 1/(1+x2) Formula 1/(1+x2) integral formula: The integration formula of 1/(1+x2) is provided below. ∫ 1/(1+x2) dx = tan-1x+C. Integration of 1/(1+x2) Proof Now, we will prove that … Read more