Question Type 3: Integrals with an inside function and its derivative Exercises

Evaluate the integral $\int \frac{2x}{(1+3x^2)^3} dx$

Evaluate the integral $\int \frac{2x}{\sqrt{1+x^2}} dx$

Evaluate the integral $\int x^2 e^{x^3} dx$

Evaluate the integral $\int \frac{6x^5}{(1+x^6)^2} dx$

Evaluate the integral $\int x \cos(x^2) \, dx$

Evaluate the integral $\int \frac{3x^2}{(x^3+1)^4} dx$

Evaluate the integral $\int 4x(3+x^2)^5 \text{d}x$.

Evaluate the integral $\int \sin(4x) \, dx$.

Evaluate the integral $\int 5e^{5x} dx$

Evaluate the integral $\int x^3\sqrt{x^4+1} \, dx$.

Evaluate the integral $\int 6x e^{3x^2} dx$

Evaluate the integral $\int (4x-2)e^{2x^2-2x} dx$