Constant Multiple Integration Rule: If a function is multiplied by a constant then the constant can be multiplied by the integral of the function {eq}\int 3f(x) dx = 3\int f(x) dx {/eq} Power Rule of Integration: For an integral of a variable x raised to a power, the anti-deriva...
Explore the steps in integration by substitution. Learn the importance of integration with the chain rule and see the u-substitution formula with various examples. Related to this Question Find the integral of sec^(-1)(sqrt x) dx. Find the integral: integral of ...
Answer and Explanation:1 Begin by simplifying the integrand, then use the Power Rule, proceed as follows: {eq}\begin{array}{l} \displaystyle{\int {\frac{{({x^3}) + ({x^2}) -... Learn more about this topic: Integration Problems in Calculus | Examples & Solution...
35K Learn the work done formula and understand the application of work integral in the work done formula with examples problems using calculus. Related to this Question Evaluate the indefinite integral: integral arctan (x^7) dx. Evaluate the indefinite integral. x arctan (4x) dx ...
Integral Examples & Functions FunctionIntegralExplanation 1/xln |x| + CThe integral of 1/x with respect to x is the natural logarithm of the absolute value of x. 2^x2^x/ln(2) + CUsing the formula for a^x with a = 2. 2xx^2 + CUsing the power rule for integration. ...
Apply the Power Rule:2x2 =2sin(d)2x2 Simplify2sin(d)2x2:x2sin(d) =x2sin(d) Add a constant to the solution=x2sin(d)+C Enter your problem Popular Examples d/(dt)(\sqrt[7]{t}+6sqrt(t^7))integral of 1/((2x-1)(x+3))∫(2x−1)(x+3)1dx(\partial)/...
Examples >>> from sympy import exp, sin, cos >>> from sympy.integrals.manualintegrate import integral_steps >>> from sympy.abc import x >>> print(repr(integral_steps(exp(x) / (1 + exp(2 * x)), x))) URule(u_var=_u, u_func=exp(x), constant=1, substep=ArctanRule(context=...
Rule: Integration by PartsPartial IntegrationSome Other ExamplesPartial Integration of DifferentialsRemarks on Integration TechniquesA Word of CautionExercisesHigher Order Approximations, Part 2: Taylor's TheoremAn Application of Integration by PartsTaylor Series of Elementary Transcendental FunctionsPower Series...
Simplify−31⋅6(2−3x)6:−181(2−3x)6 =−181(2−3x)6 Add a constant to the solution=−181(2−3x)6+C Popular Examples Frequently Asked Questions (FAQ) What is the integral of (2-3x)^5 ? The integral of (2-3x)^5 is -1/18 (2-3x)^6+C...
Integral formulas: 1. Power rule: {eq}\displaystyle \int {{y^n}} dy = \frac{{{y^{n + 1}}}{{n + 1}} + C\\ {/eq} 2. {eq}\displaystyle \int {\sin (y)dy = - \cos (y) + C} {/eq} 3. {eq}\displaystyle \int {cos(y)dy = \sin (y) + C} {/eq} ...