What is f(x) = int x+3xsqrt(x^2+1) dx if f(2) = 7 ? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer Eddie Jul 2, 2016 \implies f(x) = x^2/2+(x^2+1)^{3/2} + 5(1- sqrt5) Explanation: f(x) = int x+3xsqrt(x^2+1) dx noting the pattern D ( alpha (x^2+1)^{3/2} ) = alpha 3/2 (x^2+1)^{1/2} 2x = 3 alpha x (x^2+1)^{1/2} so here alpha = 1 \implies f(x) = x^2/2+(x^2+1)^{3/2} +C 7= 2+(5)^{3/2} +C implies C = 5(1- sqrt5) \implies f(x) = x^2/2+(x^2+1)^{3/2} + 5(1- sqrt5) Answer link Related questions How do you find the constant of integration for intf'(x)dx if f(2)=1? What is a line integral? What is f(x) = int x^3-x if f(2)=4 ? What is f(x) = int x^2+x-3 if f(2)=3 ? What is f(x) = int xe^x if f(2)=3 ? What is f(x) = int x - 3 if f(2)=3 ? What is f(x) = int x^2 - 3x if f(2)=1 ? What is f(x) = int 1/x if f(2)=1 ? What is f(x) = int 1/(x+3) if f(2)=1 ? What is f(x) = int 1/(x^2+3) if f(2)=1 ? See all questions in Evaluating the Constant of Integration Impact of this question 1368 views around the world You can reuse this answer Creative Commons License