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Integration of (ax+b)/(cx+d): Formula, Proof

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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

Integration of 1/x | Integral of 1/x

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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

Integration of 2^x | 2^x Integration

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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

Derivative of x^x [x to the power x] | d/dx(x^x)

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The derivative of xx is equal to xx(1+ln x). That is, d/dx(xx)=xx(1+ln x). This can be proved by the logarithmic differentiation. Here, ln=loge. In this post, we will learn how to find the derivative of x to the x. Derivative of xx Formula The formula of xx derivative is given by d/dx(xx)=xx(1+ln x) Derivative of … Read more

How to Integrate 1/(1+x^2) | Integration of 1/(1+x^2)

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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+x^2) is provided below. ∫ 1/(1+x2) dx = tan-1x+C. Integration of 1/(1+x2) Proof Now, we will prove that … Read more

Integration of cosecx: Formula, Proof | Cosecx Integration

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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

Integration of secx: Formula, Proof | Secx Integration

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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

Integration of cotx: Formula, Proof | cotx Integration

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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

Integration of tanx: Formula, Proof | tanx Integration

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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