Answer to: Evaluate the indefinite integral. Integral of sinh^2 x cosh x dx. By signing up, you'll get thousands of step-by-step solutions to your...
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Integration of Exponential and Logarithmic Functions: Methods and formulas to integrate functions like e^x, ln(x), etc. Integration of Hyperbolic Functions: Techniques for integrating functions like sinh(x), cosh(x), etc. Linearity of the Integral: The principle that the integral of a sum is ...
To compute the integral of the hyperbolic tangent function, follow these steps: 1.Identify the integral: We want to compute∫tanh(x)dx. 2.Recall the definition oftanh(x): The hyperbolic tangent function is defined as: wheresinh(x)=ex−e−x2andcosh(x)=ex+e−x2. ...
Integrate. Simplify your answer. Integral of (x - x^2) sinh(2x) dx. Evaluate the following integral: \int_{-1}^{1} t(1-t)^2 dt. Integrate the following expression: integral 8z^3 - 24/sqrt(z^4 - 12z) dz Integrate the following expression: integral 4z - 8/sqrt(z^2 - 4z...
=12∫∞0lnxsinhxcosh2xdx−12∫∞0lnxcosh2xdx=I1+I2(1)(1)=12∫0∞lnxsinhxcosh2xdx−12∫0∞lnxcosh2xdx=I1+I2 Adding and extracting an additional term and integrating by part the first term 2I1=∫∞0lnx(sinhxcosh2x−e−x)dx+∫∞0lnxe−xdx2I1=∫0...
Complicated Integral of arccosAsk Question Asked 1 year, 1 month ago Modified 1 year, 1 month ago Viewed 104 times 2 Let R>r>0R>r>0 be constants. I'm trying to work out the following integral:∫RR−rarccos(cosh(y)cosh(r)−cosh(R)sinh(y)sinh(r))sinh(y)dy.∫R−rRarccos...
∫0∞ln(1+x+1+x2 )1+x2 dx⏟x→sinhx+12∫01lnx1+x2 dx=∫0∞ln(1+ex)ex+e−x dx⏟e−x→x+12∑n=0∞(−)n∫01x2nlnx dx=∫01ln(1+x)−lnx1+x2 dx−12∑n=0∞(−)n(2n+1)2...
Evaluate the integral: integral of 3*tan^3(x)sec^3(x) dx. Evaluate the integral: integral (x^2-9x+5) dx Evaluate the integral: integral cosh^4 x sinh^3 x dx. Evaluate the integral: integral of 7*cos^3(2x) dx. Evaluate the integral: integral 5 dx / 5x + 3. ...
Integral of (x - x^2) sinh(2x) dx. Integrate the integral of dx/(sqrt(16 - x^2))^3. Integrate the Definite integral: \int_0^1 x^2 \sqrt {2 + x}dx Integrate the indefinite integral. \int(x+1)^{\frac{1}{2dx Integrate. \int_0^{2\pi} \int_0^{\pi} \cos^2(\phi)\...